ALBERT

Beschreibung:    The dynamic behaviors of a dry friction oscillator with shape memory alloy (SMA) are investigated. Motion equations of the system are formulated by the restoring force of the oscillator in terms of a polynomial constitutive model dependent mainly on the temperature. The vibration response of the system and the influence of the temperature are investigated. It is shown that chaotic motions can be observed and dramatically changed by temperature characteristics. Moreover, some sliding bifurcations are also discovered and influenced by the temperature. Compared with conventional dry friction elastic oscillators, the dry friction SMA oscillator presents much richer dynamic behavior caused by pseudo-elasticity, and vibration reduction can be achieved through the shape memory property of SMA restraints. Content Type Journal Article Category Original Paper Pages 1-17 DOI 10.1007/s11071-012-0353-y Authors Shihui Fu, Department of Mathematics, Zhengzhou University, Zhengzhou, Henan 450001, P.R. China Qishao Lu, Department of Dynamics and Control, Beihang University, Beijing, 100191 P.R. China Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung: Erratum to: A delayed predator–prey model with strong Allee effect in prey population growth Content Type Journal Article Category Erratum Pages 1-1 DOI 10.1007/s11071-012-0347-9 Authors Pallav Jyoti Pal, Department of Mathematics, Dumkal Institute of Engineering & Technology, Basantapur, Murshidabad 742406, India Tapan Saha, Department of Mathematics, Haldia Government College, East Midnapore, 721657 India Moitri Sen, Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur, 208016 India Malay Banerjee, Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur, 208016 India Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    An impact oscillator is a non-smooth dynamical system with discontinuous state jumps whose dynamical behavior illustrates a variety of non-linear phenomena including a grazing bifurcation. This specific phenomenon is difficult to analyze because it coincides with an infinite stretching of the phase space in the neighborhood of the grazing orbit, resulting in the well-known problem of the square-root singularity of the Jacobian of the discrete-time map. A novel Takagi–Sugeno fuzzy model-based approach is presented in this paper to model a hard impacting system as a non-smooth dynamical system including discontinuous jumps. Employing non-smooth Lyapunov theory, the structural stability of the system is analyzed to predict the onset of the destabilizing chaotic behavior. The proposed stability results, formulated as a Linear Matrix Inequality (LMI) problem, demonstrate how the new method can detect the loss of stability just before the grazing bifurcation. Content Type Journal Article Category Original Paper Pages 1-17 DOI 10.1007/s11071-012-0348-8 Authors Kamyar Mehran, School of Electrical, Electronic and Computer Engineering, Newcastle University, NE1 7RU Newcastle, England, UK Bashar Zahawi, School of Electrical, Electronic and Computer Engineering, Newcastle University, NE1 7RU Newcastle, England, UK Damian Giaouris, School of Electrical, Electronic and Computer Engineering, Newcastle University, NE1 7RU Newcastle, England, UK Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    Chaotic systems in practice are always influenced by some uncertainties and external disturbances. This paper investigates the problem of practical synchronization of fractional-order chaotic systems. Based on Lyapunov stability theory and a fractional-order differential inequality, a modified adaptive control scheme and adaptive laws of parameters are developed to robustly synchronize coupled fractional-order chaotic systems with unknown parameters and uncertain perturbations. This synchronization approach is simple, global and theoretically rigorous. Simulation results for two fractional-order chaotic systems are provided to illustrate the effectiveness of the proposed scheme. Content Type Journal Article Category Original Paper Pages 1-10 DOI 10.1007/s11071-011-0320-z Authors Ruoxun Zhang, College of Physics Science and Information Engineering, Hebei Normal University, Shijiazhuang, 050016 P.R. China Shiping Yang, College of Physics Science and Information Engineering, Hebei Normal University, Shijiazhuang, 050016 P.R. China Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    In this paper, spatial patterns of a Holling–Tanner predator-prey model subject to cross diffusion, which means the prey species exercise a self-defense mechanism to protect themselves from the attack of the predator are investigated. By using the bifurcation theory, the conditions of Hopf and Turing bifurcation critical line in a spatial domain are obtained. A series of numerical simulations reveal that the typical dynamics of population density variation is the formation of isolated groups, such as spotted, stripe-like, or labyrinth patterns. Our results confirm that cross diffusion can create stationary patterns, which enrich the finding of pattern formation in an ecosystem. Content Type Journal Article Category Original Paper Pages 1-8 DOI 10.1007/s11071-012-0374-6 Authors Gui-Quan Sun, Department of Mathematics, North University of China, Taiyuan, Shan’xi 030051, People’s Republic of China Zhen Jin, Department of Mathematics, North University of China, Taiyuan, Shan’xi 030051, People’s Republic of China Li Li, Department of Mathematics, North University of China, Taiyuan, Shan’xi 030051, People’s Republic of China Mainul Haque, Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD UK Bai-Lian Li, Ecological Complexity and Modeling Laboratory, Department of Botany and Plant Sciences, University of California, Riverside, CA 92521-0124, USA Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    In this paper, a decentralized adaptive control scheme for multi-robot coverage is proposed. This control method is designed based on centroidal Voronoi configuration integrated with robust adaptive fuzzy control techniques. We consider simple single integrator mobile robots used for covering dynamical environments, where an adaptive fuzzy logic system is used to approximate the unknown parts of control law. A robust coverage criterion is used to attenuate the adaptive fuzzy approximation error and measurement noises to a prescribed level. Therefore, the robots motion is forced to obey solutions of a coverage optimization problem. The advantages of the proposed controller can be listed as robustness to external disturbances, computation uncertainties, and measurement noises, while applicability on dynamical environments. A Lyapunov-function based proof is given of robust stability, i.e. convergence to the optimal positions with bounded error. Finally, simulation results are demonstrated for a swarm coverage problem simultaneous with tracking mobile intruders. Content Type Journal Article Category Original Paper Pages 1-11 DOI 10.1007/s11071-012-0340-3 Authors Mostafa Jahangir, Young Researchers Club, Sepidan Branch, Islamic Azad University, Sepidan, Iran Siavash Khosravi, Young Researchers Club, Sepidan Branch, Islamic Azad University, Sepidan, Iran Hossein Afkhami, Department of Electronics, Sepidan Branch, Islamic Azad University, Sepidan, Iran Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    This paper studies the problem of the robustly exponential stabilization for uncertain Markovian jump systems with mode-dependent time-varying state delays. The contribution of this paper is two-fold. Firstly, by constructing a modified Lyapunov functional and using free-weighting matrices technique, some delay-dependent robustly exponential stability criteria of such systems are obtained in terms of linear matrix inequalities (LMIs), which are less conservative than some existing ones. Secondly, a state feedback controller is designed, which can guarantee the robustly exponential stability of the uncertain closed-loop systems. Some illustrative numerical examples are given to demonstrate the reduced conservatism and applicability of the obtained results. Content Type Journal Article Pages 1-17 DOI 10.1007/s11071-012-0324-3 Authors Huabin Chen, Department of Mathematics, Nanchang University, Nanchang, 330031 Jiangxi Province, P.R. China Chuanxi Zhu, Department of Mathematics, Nanchang University, Nanchang, 330031 Jiangxi Province, P.R. China Peng Hu, School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074 Hubei Province, P.R. China Yong Zhang, College of Information Science and Technology, Wuhan University of Science and Technology, Wuhan, 430081 Hubei Province, P.R. China Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    This paper undertakes an analysis of a double Hopf bifurcation of a maglev system with time-delayed feedback. At the intersection point of the Hopf bifurcation curves in velocity feedback control gain and time delay space, the maglev system has a codimension 2 double Hopf bifurcation. To gain insight into the periodic solution which arises from the double Hopf bifurcation and the unfolding, we calculate the normal form of double Hopf bifurcation using the method of multiple scales. Numerical simulations are carried out with two pairs of feedback control parameters, which show different unfoldings of the maglev system and we verify the theoretical analysis. Content Type Journal Article Category Original Paper Pages 1-7 DOI 10.1007/s11071-011-0317-7 Authors Lingling Zhang, Department of Information Technology, Hunan Women’s University, Changsha, Hunan 410004, P.R. China Zhizhou Zhang, College of Aerospace and Materials Engineering, National University of Defense Technology, Changsha, Hunan 410073, P.R. China Lihong Huang, Department of Information Technology, Hunan Women’s University, Changsha, Hunan 410004, P.R. China Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    The various cases of synchronization in two identical hyperchaotic Lorenz systems with time delay are studied. Based on Lyapunov stability theory, the sufficient conditions for achieving synchronization of two identical hyperchaotic Lorenz systems with time delay are derived, and a simple scheme only with a single linear controller is proposed. When the parameters in the response system are known, the alternating between complete synchronization and hybrid synchronization (namely, coexistence of antiphase and complete synchronization) is observed with the control feedback gain varying. Furthermore, when the parameters in the response system are unknown, for the same feedback controller, the complete synchronization and the hybrid synchronization can be obtained, respectively, as the associated parameters updated laws of the unknown parameters are chosen. Numerical simulation results are presented to demonstrate the proposed chaos synchronization scheme. Content Type Journal Article Category Original Paper Pages 1-14 DOI 10.1007/s11071-012-0339-9 Authors Xuerong Shi, School of Mathematical Sciences, Yancheng Teachers University, Yancheng, 224002 China Zuolei Wang, School of Mathematical Sciences, Yancheng Teachers University, Yancheng, 224002 China Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    This paper deals with the adaptive control problem of the unforced generalized Korteweg–de Vries–Burgers (GKdVB) equation when the spatial domain is [0,1]. Three adaptive control laws are designed for the GKdVB equation when either the kinematic viscosity ν or the dynamic viscosity μ is unknown, or when both viscosities ν and μ are unknowns. Using the Lyapunov theory, the L 2 -global exponential stability of the solutions of this equation is shown for each of the proposed control laws. Also, numerical simulations based on the Finite Element method (FEM) are given to illustrate the analytical results. Content Type Journal Article Category Original Paper Pages 1-17 DOI 10.1007/s11071-012-0343-0 Authors N. Smaoui, Department of Mathematics, Kuwait University, P.O. Box 5969, Safat, 13060 Kuwait A. El-Kadri, Department of Mathematics, Kuwait University, P.O. Box 5969, Safat, 13060 Kuwait M. Zribi, Department of Electrical Engineering, Kuwait University, P.O. Box 5969, Safat, 13060 Kuwait Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    In this article, a novel dynamic system, the fractional-order complex Lorenz system, is proposed. Dynamic behaviors of a fractional-order chaotic system in complex space are investigated for the first time. Chaotic regions and periodic windows are explored as well as different types of motion shown along the routes to chaos. Numerical experiments by means of phase portraits, bifurcation diagrams and the largest Lyapunov exponent are involved. A new method to search the lowest order of the fractional-order system is discussed. Based on the above result, a synchronization scheme in fractional-order complex Lorenz systems is presented and the corresponding numerical simulations demonstrate the effectiveness and feasibility of the proposed scheme. Content Type Journal Article Category Original Paper Pages 1-17 DOI 10.1007/s11071-012-0656-z Authors Chao Luo, Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian, 116024 China Xingyuan Wang, Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian, 116024 China Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    This paper studies the characteristics of a series of complex systems, which are in combination of interest rate, investment, and price index parameters meeting the condition c − b − abc ≥0, including stable node, saddle points, bifurcation, Hopf bifurcation, and chaos, and the corresponding mathematical expressions of Lyapunov index are given. Based on this, we perform complexity analysis of the system and study the change circumstances of Lyapunov index when one or two parameters synchronously change. Numerical simulation results verify the theoretical analysis and conclusion. The results of this economic and financial system provide reference to practical problems, and have a positive effect on the actual application of the system of this type. Content Type Journal Article Category Original Paper Pages 1-14 DOI 10.1007/s11071-012-0336-z Authors Junhai Ma, College of Management and Economics, Tianjin University, Tianjin, 300072 China Hamza I. Bangura, College of Management and Economics, Tianjin University, Tianjin, 300072 China Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    In this paper, center conditions and bifurcation of limit cycles at the nilpotent critical point in a class of quintic polynomial differential system are investigated. With the help of the computer algebra system MATHEMATICA, the first 11 quasi-Lyapunov constants are deduced. As a result, sufficient and necessary conditions in order to have a center are obtained. The fact that there exist 11 small amplitude limit cycles created from the three-order nilpotent critical point is also proved. Henceforth, we give a lower bound of cyclicity of three-order nilpotent critical point for quintic Lyapunov systems. The results of Jiang et al. (Int. J. Bifurcation Chaos 19:2107–2113, 2009 ) are improved. Content Type Journal Article Category Original Paper Pages 1-10 DOI 10.1007/s11071-012-0653-2 Authors Feng Li, School of Science, Linyi University, Linyi, 276005 Shandong, P.R. China Miao Wang, Department of Mathematics, Swansea University, Singleton Park, SA2 8PP UK Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    Complex networks have been judiciously developed during the last decades. Much attention has been given to investigate the synchronization of complex networks in recent years. In this paper, by constructing a drive network and a suitable impulsively controlled slave network, several synchronization criteria for the uncertain complex networks have been obtained based on the adaptive-impulsive method. The tracking parameters are realized simultaneously as the synchronization occurs. Particularly, our hypotheses and the proposed adaptive-impulsive control laws for network synchronization are simple and can be readily applied in practical applications. Finally, numerical simulations are provided to illustrate the effectiveness of the proposed synchronization criteria. Content Type Journal Article Category Original Paper Pages 1-7 DOI 10.1007/s11071-012-0665-y Authors Qunjiao Zhang, College of Mathematics and Computer Science, Wuhan Textile University, Wuhan, 430073 China Juan Luo, College of Mathematics and Computer Science, Wuhan Textile University, Wuhan, 430073 China Li Wan, College of Mathematics and Computer Science, Wuhan Textile University, Wuhan, 430073 China Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    In this paper, we use the optimal velocity model, full velocity difference model, full velocity and acceleration difference model, and the car-following model with consideration of the traffic interruption probability to study the electric vehicle’s electricity energy consumption. The numerical results show that the electric vehicle’s electricity energy consumption is most stable in the fourth model and that the fourth model can reduce the electric vehicle’s electricity energy consumption. Content Type Journal Article Category Original Paper Pages 1-7 DOI 10.1007/s11071-012-0663-0 Authors Shichun Yang, School of Transportation Science and Engineering, Beihang University, Beijing, 100191 China Cheng Deng, School of Transportation Science and Engineering, Beihang University, Beijing, 100191 China Tieqiao Tang, School of Transportation Science and Engineering, Beihang University, Beijing, 100191 China Yongsheng Qian, School of Traffic and Transportation, Lanzhou Jiao Tong University, Lanzhou, Gansu 730070, China Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    This article addresses the reliable problem for networked control systems with actuator failure. By combining the Lyapunov stability theory, the linear matrix inequality (LMI) optimization technique, and structural constraints, an optimal reliable feedback controller is established to guarantee asymptotically stable even though some control component (actuator) failures occur. Finally, an illustrative example is provided to demonstrate the effectiveness of the results developed in this paper. Content Type Journal Article Category Original Paper Pages 1-9 DOI 10.1007/s11071-012-0671-0 Authors Yi-You Hou, Department of Electrical Engineering, Far East University, Tainan, 744 Taiwan Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    This paper deals with the design of nonlinear controllers for the wing-rock phenomenon of a delta wing aircraft. A fifth order dynamic model is used to describe this phenomenon. A state transformation is introduced such that the transformed dynamic model is in a form which is suitable for a variety of control designs. A feedback linearization control scheme and a sliding-mode control (SMC) scheme are then proposed to suppress wing rock oscillations. It is shown that the two controllers successfully suppress the undesired oscillations and guarantee the asymptotic convergence of all system trajectories to their desired values. The effectiveness of the proposed controllers is verified through simulation studies. Content Type Journal Article Category Original Paper Pages 1-10 DOI 10.1007/s11071-012-0662-1 Authors Mohamed Zribi, Electrical Engineering Department, College of Engineering and Petroleum, Kuwait University, P.O. Box 5969, Safat, 13060 Kuwait Saleh Alshamali, Electrical Engineering Department, College of Engineering and Petroleum, Kuwait University, P.O. Box 5969, Safat, 13060 Kuwait Mohamed Al-Kendari, Electrical Engineering Department, College of Engineering and Petroleum, Kuwait University, P.O. Box 5969, Safat, 13060 Kuwait Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    We consider asymptotic solutions for nonlinear beams that can be described by a fourth order hyperbolic equation with an integral nonlinearity and some space and time dependent coefficients. These coefficients can describe varying mass and rigidity perturbations. A two-time scales perturbation method reduces this complicated equation to an infinite-dimensional Hamiltonian system for the Fourier modes. An analysis of this system shows that the corresponding dynamics is quasi-periodic and periodic in time if the coefficients are constant. For non-constant coefficients the dynamics changes significantly. For some special non-constant coefficients the Hamiltonian dynamics can be simplified. We obtain a simpler finite-dimensional system. Numerical simulations show existence of new interesting dynamical effects due to resonances between some Fourier modes. These resonances can lead to large oscillations, even for small nonlinearities. The phase portraits which correspond to these resonance cases will also be presented. Content Type Journal Article Category Original Paper Pages 1-22 DOI 10.1007/s11071-012-0661-2 Authors A. K. Abramian, Institute of Problems in Mechanical Engineering, Russian Academy of Sciences, V.O., Bol’shoy pr., 61, 199178 St. Petersburg, Russia W. T. van Horssen, Department of Applied Mathematical Analysis, Faculty EEMCS, Delft University of Technology, Mekelweg 4, 2628 CD Delft, Netherlands S. A. Vakulenko, Institute of Problems in Mechanical Engineering, Russian Academy of Sciences, V.O., Bol’shoy pr., 61, 199178 St. Petersburg, Russia Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    In this paper, a new adaptive fuzzy sliding mode (AFSM) observer is proposed which can be used for a class of MIMO nonlinear systems. In the proposed algorithm, the zero-input dynamics of the plant could be unknown. In this method, a fuzzy system is designed to estimate the nonlinear behavior of the observer. The output of fuzzy rules are tuned adaptively, based on the observer error. The output connection matrix is used to combine the observer errors of individual subsystems. A robust term, which is designed based on the sliding mode theory, is added to the observer to compensate the fuzzy estimation error. The estimation error bound is adjusted by an adaptive law. The main advantage of the proposed observer is that, unlike many of the previous works, the measured outputs is not limited to the first entries of a canonical-form state vector. The proposed observer estimates the closed-loop state tracking error asymptotically, provided that the output gain matrix includes Hurwitz coefficients. The chattering is eliminated by using boundary layers around the sliding surfaces and the observer convergence is proved using a Lyapunov-based approach. The proposed method is applied on a real multilink robot manipulator. The performance of the observer shows its effectiveness in the real world. Content Type Journal Article Category Original Paper Pages 1-11 DOI 10.1007/s11071-012-0602-0 Authors Alireza Gholami, Digital Control Laboratory, School of Mechanical Engineering, Iran University of Science and Technology, Narmak, Tehran, 16844 Iran Amir H. D. Markazi, Digital Control Laboratory, School of Mechanical Engineering, Iran University of Science and Technology, Narmak, Tehran, 16844 Iran Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    This study is focused on dynamic modeling of planar multibody systems with multiple deep groove ball bearing joints, in which the radial clearance, contact deformation, and bearing kinematics are included. By using the approach presented, the variation of the joint reaction force and the dynamic load on each ball element in bearings can be simulated. The deep groove ball bearing joints are modeled by introducing a nonlinear force system, which takes into account the contact elastic deformations between the ball elements and the raceways. The contact force is calculated by the Hertzian contact deformation theory that accounts for the geometrical and material properties of the contacting bodies. A planar slider-crank mechanism with two deep groove ball bearing joints is chosen as an example to demonstrate the application of the methodologies presented in this paper. In this model, one bearing locates at the joint between the ground and crank, while the other one locates at the joint between the crank and connecting rod. By numerical calculation, the dynamic load distribution characteristics of bearings under real mechanism movement conditions are simulated. From the results, it can be concluded that the dynamic load on each rolling element varies differently and belongs to a variable load with the change of mechanism configuration. Load characteristic analysis is the foundation of developing research on the fatigue life and reliability of bearings. This study will provide a key mechanical support for the performance evaluation, dynamic design, and geometrical parameter optimization of the joint rolling element bearings. Content Type Journal Article Category Original Paper Pages 1-17 DOI 10.1007/s11071-012-0606-9 Authors Li-xin Xu, School of Mechanical Engineering, Tianjin University of Technology and Education, Tianjin, 300222 China Yong-gang Li, School of Mechanical Engineering, Tianjin University of Technology and Education, Tianjin, 300222 China Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    The aim of this paper is to derive a set of sufficient conditions for controllability of nonlinear fractional dynamical system of order 1〈 α 〈2 in finite dimensional spaces. The results are obtained using the Schauder fixed point theorem. Examples are included to verify the result. Content Type Journal Article Category Original Paper Pages 1-8 DOI 10.1007/s11071-012-0612-y Authors K. Balachandran, Department of Mathematics, Bharathiar University, Coimbatore, 641 046 India V. Govindaraj, Department of Mathematics, Bharathiar University, Coimbatore, 641 046 India L. Rodríguez-Germá, Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna, Tenerife, Spain J. J. Trujillo, Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna, Tenerife, Spain Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    In cryptographic systems, the encryption process relies on the nonlinear mapping of original data or plaintext to the secure data. The mapping of data is facilitated by the application of the substitution process embedded in the cipher. It is desirable to have resistance against differential cryptanalysis, which assists in providing clues about the composition of keys, and linear secret system, where a simple approximation is created to emulate the original cipher characteristics. In this work, we propose the use of nonlinear functional chaos-based substitution process which employs a continuous time Lorenz system. The proposed substitution system eliminates the need of independent round keys in a substitution-permutation network. The performance of the new substitution box is evaluated by nonlinearity analysis, strict avalanche criterion, bit independence criterion, linear approximation probability, and differential approximation probability. Content Type Journal Article Category Original Paper Pages 1-9 DOI 10.1007/s11071-012-0621-x Authors Majid Khan, Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan Tariq Shah, Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan Hasan Mahmood, Department of Electronics, Quaid-i-Azam University, Islamabad, Pakistan Muhammad Asif Gondal, Department of Sciences and Humanities, National University of Computer and Emerging Sciences, Islamabad, Pakistan Iqtadar Hussain, Department of Sciences and Humanities, National University of Computer and Emerging Sciences, Islamabad, Pakistan Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    In this study, an iterative method based on harmonic balance for the period-one rotation of parametrically excited pendulum is proposed. Based on the definition of the period-one rotating orbit, the exact form of the solution can be obtained using the Fourier series. An iterative harmonic balance process is proposed to estimate the coefficients in the exact solution form. The general formula for each iteration step is presented. The method is evaluated using two criteria, which are the system energy error and the global residual error. The performance of the proposed method is compared with the results from multiscale method and perturbation method. The numerical results obtained with the Dormand–Prince method (ODE45 in MATLAB©) are used as the baseline of the evaluation. Content Type Journal Article Category Original Paper Pages 1-12 DOI 10.1007/s11071-012-0631-8 Authors Hui Zhang, Department of Civil and Environmental Engineering, University of Hawaii at Mānoa, Honolulu, HI 96822, USA Tian-Wei Ma, Department of Civil and Environmental Engineering, University of Hawaii at Mānoa, Honolulu, HI 96822, USA Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    Steady-state periodic responses of nonlinear coupled planar motions are investigated for transporting beams in the supercritical transport speed ranges. The straight equilibrium configuration bifurcates into multiple equilibrium positions in the supercritical regime. The finite-difference schemes are developed to calculate the non-trivial static equilibrium and the steady-state response under simply supported or clamped boundary conditions. The forced vibration is assumed to be spatially uniform and temporally simple harmonic. Based on the long time series, the steady-state transversal amplitudes of nonlinear planar motions are recorded with changing load frequencies. A resonance exists if the external load frequency approaches the fundamental frequency. The effects of material parameters and vibration amplitude on the resonance responses are investigated. The coupled planar model can be reduced to two nonlinear models on transversal vibrations, an integro-partial–differential equation and a partial–differential one. Numerical examples are displayed for the pros and cons between the two transversal models. It is also revealed that the increased axial speed converts the hardening-type behavior into the softening-type one. Content Type Journal Article Category Original Paper Pages 1-14 DOI 10.1007/s11071-012-0629-2 Authors Guo-Ce Zhang, Shanghai Institute of Applied Mathematics and Mechanics, Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai, 200072 China Hu Ding, Shanghai Institute of Applied Mathematics and Mechanics, Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai, 200072 China Li-Qun Chen, Shanghai Institute of Applied Mathematics and Mechanics, Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai, 200072 China Shao-Pu Yang, Shijiazhuang Tiedao University, Shijiazhuang, 050043 China Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    To guarantee secure communication, many maps-based key agreement protocols have been proposed. Due to inherent tamper-resistance, most of them are based on smart cards. Unfortunately, the cost of cards and readers makes these protocols costly. In the real world, common storage devices, such as universal serial bus (USB) thumb drives, portable HDDs, mobile phones, and laptop or desktop PCs, are widely used, and they are much cheaper or more convenient for storing user authentication information. These devices do not provide tamper-resistance; it is a challenge to design a secure authentication protocol using these kinds of memory devices. In this paper, we will propose a maps-based key agreement protocol without using smart cards. According to our analysis, the proposed protocol guarantees mutual authentication, and also resists different attacks. Therefore, our protocol is suitable even for practical applications. Content Type Journal Article Category Original Paper Pages 1-6 DOI 10.1007/s11071-012-0628-3 Authors Peng Gong, National Key Laboratory of Mechatronic Engineering and Control, School of Mechatronical Engineering, Beijing Institute of Technology, Beijing, China Ping Li, National Key Laboratory of Mechatronic Engineering and Control, School of Mechatronical Engineering, Beijing Institute of Technology, Beijing, China Wenbo Shi, Department of Electronic Engineering, Northeastern University at Qinhuangdao, Qinhuangdao, China Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    Recently, a colour image encryption algorithm based on chaos was proposed by cascading two position permutation operations and one substitution operation, which are all determined by some pseudo-random number sequences generated by iterating the logistic map. This paper evaluates the security level of this encryption algorithm and finds that the position permutation-only part and the substitution part can be separately broken with only ⌈(log 2 (3 MN ))/8⌉ and 2 chosen plain-images, respectively, where MN is the size of the plain-image. The effectiveness of the proposed chosen-plaintext attack is supported by concise theoretical analyses, and is verified by experimental results. Content Type Journal Article Category Original Paper Pages 1-6 DOI 10.1007/s11071-012-0626-5 Authors Chengqing Li, College of Information Engineering, Xiangtan University, Xiangtan, 411105 Hunan, China Leo Yu Zhang, School of Mathematics and Computational Science, Xiangtan University, Xiangtan, 411105 Hunan, China Rong Ou, College of Information Engineering, Xiangtan University, Xiangtan, 411105 Hunan, China Kwok-Wo Wong, Department of Electronic Engineering, City University of Hong Kong, Hong Kong, China Shi Shu, School of Mathematics and Computational Science, Xiangtan University, Xiangtan, 411105 Hunan, China Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    In this paper, a generalized Darbo’s fixed-point theorem associated with Hausdorff measure of noncompactness is established. Then we apply this new variant fixed-point theorem to study some fractional differential equations in Banach spaces via the technique of measure of noncompactness. Many novel existence and uniqueness results for solutions are obtained under the more general conditions. Content Type Journal Article Category Original Paper Pages 1-16 DOI 10.1007/s11071-012-0452-9 Authors JinRong Wang, Department of Mathematics, Guizhou University, Guiyang, Guizhou 550025, P.R. China Yong Zhou, Department of Mathematics, Xiangtan University, Xiangtan, Hunan 411105, P.R. China Michal Fec̆kan, Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and Informatics, Comenius University, Mlynská dolina, 842 48 Bratislava, Slovakia Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    This paper is concerned with the delay-dependent synchronization criterion for stochastic complex networks with time delays. Firstly, expectations of stochastic cross terms containing the Itô integral are investigated by utilizing stochastic analysis techniques. In fact, in order to obtain less conservative delay-dependent conditions for stochastic delay systems including stochastic complex (or neural) networks with time delays, how to deal with expectations of these stochastic cross terms is an important problem, and expectations of these stochastic terms were not dealt with properly in many existing results. Then, based on the investigation of expectations of stochastic cross terms, this paper proposes a novel delay-dependent synchronization criterion for stochastic delayed complex networks. In the derivation process, the mathematical development avoids bounding stochastic cross terms. Thus, the method leads to a simple criterion and shows less conservatism. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed approach. Content Type Journal Article Category Original Paper Pages 1-11 DOI 10.1007/s11071-012-0627-4 Authors Bo Song, Nonlinear Dynamics Group, Department of Electrical Engineering, Yeungnam University, 214-1 Dae-Dong, Kyongsan, 712-749 Republic of Korea Ju H. Park, Nonlinear Dynamics Group, Department of Electrical Engineering, Yeungnam University, 214-1 Dae-Dong, Kyongsan, 712-749 Republic of Korea Zheng-Guang Wu, Nonlinear Dynamics Group, Department of Electrical Engineering, Yeungnam University, 214-1 Dae-Dong, Kyongsan, 712-749 Republic of Korea Ya Zhang, School of Mathematics and Physics, Xuzhou Institute of Technology, Xuzhou, Jiangsu 221000, P.R. China Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    In this paper, a new effective approach—backstepping with Ge–Yao–Chen (GYC) partial region stability theory (called BGYC in this article) is proposed to applied to adaptive synchronization. Backstepping design is a recursive procedure that combines the choice of a Lyapunov function with the design of a controller, and it presents a systematic procedure for selecting a proper controller in chaos synchronization. We further combine the systematic backstepping design and GYC partial region stability theory in this article, Lyapunov function can be chosen as a simple linear homogeneous function of states, and the controllers and the update laws of parameters shall be much simpler. Further, it also introduces less simulation error—the numerical simulation results show that the states errors and parametric errors approach to zero much more exactly and efficiently, which are compared with the original one. Two cases are presented in the simulation results to show the effectiveness and feasibility of our new strategy. Content Type Journal Article Category Original Paper Pages 1-15 DOI 10.1007/s11071-012-0605-x Authors Shih-Yu Li, Department of Biological Science and Technology, National Chiao Tung University, Hsinchu, Taiwan, Republic of China Cheng-Hsiung Yang, Department of Automatic Control, National Taiwan University of Science and Technology, Taipei City, Taiwan, Republic of China Chin-Teng Lin, Brain Research Center, National Chiao Tung University, Hsinchu, Taiwan, Republic of China Li-Wei Ko, Department of Biological Science and Technology, National Chiao Tung University, Hsinchu, Taiwan, Republic of China Tien-Ting Chiu, Department of Industrial and Systems Engineering, Chung Yuan Christian University, Chung-Li, Taiwan, Republic of China Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    The geometrically exact equations of motion about the prestressed state discussed in part 1 (i.e., the nonlinear equilibrium under centrifugal forces) are expanded in the Taylor series of the incremental displacements and rotations to obtain the third-order perturbed form. The expanded form is amenable to a perturbation treatment to unfold the nonlinear features of free undamped flapping dynamics. The method of multiple scales is thus applied directly to the partial-differential equations of motion to construct the backbone curves of the flapping modes and their nonlinear approximations when they are away from internal resonances with other modes. The effective nonlinearity coefficients of the lowest three flapping modes of elastic isotropic blades are investigated when the angular speed is changed from low- to high-speed regimes. The novelty of the current findings is in the fact that the nonlinearity of the flapping modes is shown to depend critically on the angular speed since it can switch from hardening to softening and vice versa at certain speeds. The asymptotic results are compared with previous literature results. Moreover, 2:1 internal resonances between flapping and axial modes are exhibited as singularities of the effective nonlinearity coefficients. These nonlinear interactions can entail fundamental changes in the blade local and global dynamics. Content Type Journal Article Category Original Paper Pages 1-23 DOI 10.1007/s11071-012-0619-4 Authors Hadi Arvin, Department of Mechanical Engineering, Amirkabir University of Technology, 424 Hafez Ave, Tehran, Iran Walter Lacarbonara, Dipartimento di Ingegneria Strutturale e Geotecnica, Sapienza University of Rome, Via Eudossiana 18, 00184 Roma, Italy Firooz Bakhtiari-Nejad, Department of Mechanical Engineering, Amirkabir University of Technology, 424 Hafez Ave, Tehran, Iran Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    This paper addresses stochastic synchronization issue of the four-dimensional energy resource system with stochastic noises based on partial states. By using the adaptive control approach, in the case of only parts of states are available, several sufficient conditions are derived to ensure synchronization of the nonlinear energy resource system under noise perturbation. Furthermore, robust synchronization in the presence of parameter mismatches is also considered. To be pointed out that, the important feature of the proposed method is that synchronization could be achieved through the control of only parts of available variables even with stochastic noises. Finally, a numerical example with simulation results is provided to illustrate and verify the effectiveness of the obtained results. Content Type Journal Article Category Original Paper Pages 1-10 DOI 10.1007/s11071-012-0617-6 Authors Yonghui Sun, College of Energy and Electrical Engineering, Hohai University, Nanjing, 210098 China Zhinong Wei, College of Energy and Electrical Engineering, Hohai University, Nanjing, 210098 China Guoqiang Sun, College of Energy and Electrical Engineering, Hohai University, Nanjing, 210098 China Ping Ju, College of Energy and Electrical Engineering, Hohai University, Nanjing, 210098 China Yanfang Wei, College of Energy and Electrical Engineering, Hohai University, Nanjing, 210098 China Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    We study the dynamics of a two-degrees-of-freedom (two-DOF) nonlinear oscillator representing a quarter-car model excited by a road roughness profile. Modeling the road profile by means of a harmonic function, we derive the Melnikov criterion for a system transition to chaos or escape. The analytically obtained estimations are confirmed by numerical simulations. To analyze the transient vibrations, we used recurrences. Content Type Journal Article Category Original Paper Pages 1-9 DOI 10.1007/s11071-012-0518-8 Authors Marek Borowiec, Department of Applied Mechanics, Lublin University of Technology, Nadbystrzycka 36, 20-618 Lublin, Poland Grzegorz Litak, Department of Applied Mechanics, Lublin University of Technology, Nadbystrzycka 36, 20-618 Lublin, Poland Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    An efficient and straightforward algorithm for the integration of the constrained systems is developed in the present work. Some of the fundamental issues of contact dynamics are briefly reviewed. Considering Gauss’ least constraint principle, an intuitive and effective computation method of the constraint forces is arrived at. The contact problem is solved by means of the generalized matrix inverse (GI) embedded in an appropriate algorithm and the numerical integration is event-driven. The method is applied to the study of train longitudinal dynamics which is essential for comfort and running safety. Due to the complexity of the phenomena and the presence of dry friction, the investigations have been carried out by numerical methods using regularization. Based on the non-smooth dynamics approach, in the present paper, a comprehensive model is presented. Set-value friction of Coulomb’s law type is accounted for and motion equations are formulated as a differential inclusion. Application examples are presented. Simulations demonstrate the existence of specific phenomena like stick–slip and offset in the final equilibrium position. Computational efficiency is dramatically improved compared with previous models, while computation speed is increased by at least an order of magnitude. A wide class of problems may be solved using the present method, as is pointed out in the article. Content Type Journal Article Category Original Paper Pages 1-12 DOI 10.1007/s11071-012-0515-y Authors Razvan Andrei Oprea, Railway Vehicles Engineering Department, University Politehnica of Bucharest, str. Rucar 12, s1, Bucharest, 012257 Romania Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    The main contribution of this paper is using optimal control theory for improving the convergence rate of backpropagation algorithm. In the proposed approach, the learning algorithm of backpropagation is modeled as a minimum time control problem in which the step-size of its learning factor is considered as the input of this model. In contrast to the traditional backpropagation, learning algorithms which select the step-size by trial and error, it is selected adaptively based on optimal control criterion. The effectiveness of the proposed algorithm is evaluated in two simulations: XOR and 3-bit parity . In both simulation examples, the proposed algorithm outperforms well in speed and the ability to escape from local minima. Content Type Journal Article Category Original Paper Pages 1-9 DOI 10.1007/s11071-012-0512-1 Authors Mostafa Jahangir, Young Researchers Club, Sepidan Branch, Islamic Azad University, Sepidan, Iran Mehdi Golshan, Young Researchers Club, Sepidan Branch, Islamic Azad University, Sepidan, Iran Siavash Khosravi, Young Researchers Club, Sepidan Branch, Islamic Azad University, Sepidan, Iran Hossein Afkhami, Department of Electronics, Sepidan Branch, Islamic Azad University, Sepidan, Iran Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    Cluster synchronization is an interesting issue in complex dynamical networks with community structure. In this paper, we study cluster synchronization of complex networks with non-identical systems by input-to-state stability. Some sufficient conditions that ensure cluster synchronization of complex networks are provided. We show that the cluster synchronization is difficult to achieve if there are some links among different clusters. The analysis is then extended to the case where the outer coupling strengths are adaptive. Finally, numerical simulations are given to validate our theoretical analysis. Content Type Journal Article Category Original Paper Pages 1-9 DOI 10.1007/s11071-012-0516-x Authors Junchan Zhao, College of Mathematica and Computer Science, Wuhan Textile University, Wuhan, 430073 China M. A. Aziz-Alaoui, Applied Mathematics Laboratory, University of Le Havre, 76058 Le Havre Cedex, France Cyrille Bertelle, LITIS, University of Le Havre, 76058 Le Havre Cedex, France Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    A semi-numerical method is used in order to locate the position and calculate the period of periodic orbits in a 3D composite bisymmetrical potential, in a number of resonant cases. The potential consists of a 3D harmonic oscillator and a Plummer sphere. The outcomes are compared with results found using the numerical integration of the equations of motion and the agreement is very good. This agreement strongly suggests, that semi-numerical methods can be used in order to obtain fast and reliable results regarding the position and period of the periodic orbits in 3D composite potentials with a harmonic oscillator part and different kinds of perturbations. Comparison with other methods of obtaining 3D periodic orbits is discussed. Content Type Journal Article Category Original Paper Pages 1-9 DOI 10.1007/s11071-012-0453-8 Authors Euaggelos E. Zotos, Department of Physics, Section of Astrophysics, Astronomy and Mechanics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece Nicolaos D. Caranicolas, Department of Physics, Section of Astrophysics, Astronomy and Mechanics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    A novel increased coupling-based nonlinear control strategy is proposed for underactuated overhead crane systems, which guarantees both fast trolley positioning and sufficient payload swing elimination performance. The developed controller is applicable to both regulation control and trajectory tracking control. To artificially increase the trolley-translation/payload-swing internal coupling, a payload position-like composite variable is introduced and a corresponding elegant error signal is then constructed, based on which a novel control law is designed to transform the overhead crane system into an interconnected system consisting of two subsystems with respect to (w.r.t.) the constructed error signal and the payload swing angle, respectively. Both subsystems are proven to be input-to-state stable (ISS); by invoking the small gain theorem, we show that the overall interconnected system is also ISS. LaSalle’s invariance theorem further proves that the system states asymptotically converge to the desired equilibrium point. Experimental results are included to demonstrate the feasibility and effectiveness of the proposed method and also its superior control performance over some existing schemes. Content Type Journal Article Category Original Paper Pages 1-12 DOI 10.1007/s11071-012-0519-7 Authors Ning Sun, Institute of Robotics and Automatic Information System, Nankai University, Tianjin, China Yongchun Fang, Institute of Robotics and Automatic Information System, Nankai University, Tianjin, China Xuebo Zhang, Institute of Robotics and Automatic Information System, Nankai University, Tianjin, China Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    In this paper, the problem of robust sampled-data H ∞ output tracking control is investigated for a class of fuzzy networked systems with stochastic sampling, multiplicative noise and time-varying norm-bounded uncertainties. For the sake of technical simplicity, only two different sampling periods are considered, their occurrence probabilities are given constants and satisfy Bernoulli distribution, and they can be extended to the case with multiple stochastic sampling periods. By using an input-delay method, the probabilistic system is transformed into a stochastic continuous time-delay system. A new linear matrix inequality(LMI)-based procedure is proposed for designing state-feedback controllers, which would guarantee that the closed-loop networked system with stochastic sampling tracks the output of a given reference model well in the sense of H ∞ . Conservatism is reduced by taking the probability into account. Both network-induced delays and packet dropouts have been considered. Finally, an illustrative example is given to show the usefulness and effectiveness of the proposed H ∞ output tracking design. Content Type Journal Article Category Original Paper Pages 1-17 DOI 10.1007/s11071-012-0513-0 Authors Shiping Wen, Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan, 430074 China Zhigang Zeng, Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan, 430074 China Tingwen Huang, Texas A& M University at Qatar, Doha, 5825 Qatar Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    In the present paper, two types of complex delayed dynamical networks with spatially and temporally varying state variables are proposed. The first is that all nodes in the network have the same time-varying delay. The second is that different nodes have different time-varying delays. We respectively investigate the stabilization problem of these two types of complex network models by pinning a small fraction of nodes with negative feedback controllers. With the help of Lyapunov functionals and some inequality techniques, several asymptotic stability and exponential stability conditions are established. Finally, numerical simulations are presented to illustrate the effectiveness of the results obtained here. Content Type Journal Article Category Original Paper Pages 1-18 DOI 10.1007/s11071-012-0564-2 Authors Jin-Liang Wang, Science and Technology on Aircraft Control Laboratory, School of Automation Science and Electrical Engineering, Beihang University, Beijing, 100191 China Huai-Ning Wu, Science and Technology on Aircraft Control Laboratory, School of Automation Science and Electrical Engineering, Beihang University, Beijing, 100191 China Lei Guo, Science and Technology on Aircraft Control Laboratory, School of Automation Science and Electrical Engineering, Beihang University, Beijing, 100191 China Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    This paper presents a robust adaptive sliding mode control strategy using radial basis function (RBF) neural network (NN) for a class of time varying system in the presence of model uncertainties and external disturbance. Adaptive RBF neural network controller that can learn the unknown upper bound of model uncertainties and external disturbances is incorporated into the adaptive sliding mode control system in the same Lyapunov framework. The proposed adaptive sliding mode controller can on line update the estimates of system dynamics. The asymptotical stability of the closed-loop system, the convergence of the neural network weight-updating process, and the boundedness of the neural network weight estimation errors can be strictly guaranteed. Numerical simulation for a MEMS triaxial angular velocity sensor is investigated to verify the effectiveness of the proposed adaptive RBF sliding mode control scheme. Content Type Journal Article Category Original Paper Pages 1-11 DOI 10.1007/s11071-012-0556-2 Authors Juntao Fei, Jiangsu Key Laboratory of Power Transmission and Distribution Equipment Technology, College of Computer and Information, Hohai University, Changzhou, 213022 China Hongfei Ding, Jiangsu Key Laboratory of Power Transmission and Distribution Equipment Technology, College of Computer and Information, Hohai University, Changzhou, 213022 China Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung: Erratum to: Brachistochrone with limited reaction of constraint in an arbitrary force field Content Type Journal Article Category Erratum Pages 1-2 DOI 10.1007/s11071-012-0553-5 Authors Slaviša Šalinić, Faculty of Mechanical Engineering, University of Kragujevac, Dositejeva 19, 36000 Kraljevo, Serbia Aleksandar Obradović, Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Belgrade 35, Serbia Zoran Mitrović, Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Belgrade 35, Serbia Srdjan Rusov, Faculty of Transport and Traffic Engineering, University of Belgrade, Vojvode Stepe 305, 11000 Belgrade, Serbia Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    In this paper, we implement some fast and high accuracy numerical algorithms to obtain the solitary wave solutions of generalized Pochhammer–Chree (PC) and regularized long wave (RLW) equations. We employ the discrete Fourier transform to discretize the original partial differential equations (PDEs) in space and obtain a system of ordinary differential equations (ODEs) in Fourier space which will be solved with fourth order time-stepping methods. The proposed methods are fast and accurate due to the use of the fast Fourier transform in combination with explicit fourth-order time stepping methods. For RLW equation we investigate the propagation of a single solitary and interaction of two and three solitary waves. Moreover, three invariants of motion (mass, energy, and momentum) are evaluated to determine the conservation properties of the problem, and the numerical schemes lead to accurate results. The numerical results are compared with analytical solutions and with those of other recently published methods to confirm the accuracy and efficiency of the presented schemes. Content Type Journal Article Category Original Paper Pages 1-12 DOI 10.1007/s11071-012-0634-5 Authors Akbar Mohebbi, Department of Applied Mathematics, Faculty of Mathematical Science, University of Kashan, Kashan, Iran Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    For a hip joint simulator with a 3SPS+1PS spatial parallel manipulator as the core module, a formulation based on the Kane equation was derived for the dynamic characteristics of the simulator from the kinematics analysis of the model. The relationships of the velocities and accelerations between the moving platform and active branched-chains were deduced. The velocity and angular velocity components of the moving platform were served as the generalized velocities. And the dynamic model was established by obtaining the generalized active forces and inertial forces. Then the driving forces and powers of the active branched-chains and the constraint reaction forces of the intermediate branched-chain were simulated in the numerical method. The results showed that the active driving forces of the branched-chains reached their respective maximum when the moving platform rotated into 0.13 ∘ around X -axis, 2 ∘ around Y -axis, and 18 ∘ around Z -axis. And the intermediate branched-chain needed to balance the driving and inertia forces, as well as support the moving platform and load the force of hydraulic cylinder. Therefore, the maximum constraint reaction force of the intermediate branched-chain is along the Z -axis. The research works provided a theoretical basis for the design of the active branched-chains driving system and the structural parameters of the intermediate branched-chain, as well as for the control system. Content Type Journal Article Category Original Paper Pages 1-12 DOI 10.1007/s11071-012-0635-4 Authors Gang Cheng, School of Mechanical and Electrical Engineering, China University of Mining and Technology, 221116 Xuzhou, China Xianlei Shan, School of Mechanical and Electrical Engineering, China University of Mining and Technology, 221116 Xuzhou, China Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    In this paper, the problem of controlling epileptiform spikes in a neural mass model is addressed. Considering the complication and nonlinearity of the neural mass model, a fuzzy PID controller is designed so that epileptiform spikes are quenched and the output waveform tracks an expected one. The tracking effect is analyzed by numerical simulation for a regular network of coupled neural populations. The effect of important model parameters on the control energy and the effect of the types of controlled populations on the ability to realize the tracking purpose are analyzed for the same network. Content Type Journal Article Category Original Paper Pages 1-11 DOI 10.1007/s11071-012-0638-1 Authors Xian Liu, Key Lab of Industrial Computer Control Engineering of Hebei Province, Institute of Electrical Engineering, Yanshan University, Qinhuangdao, 066004 China Huijun Liu, Key Lab of Industrial Computer Control Engineering of Hebei Province, Institute of Electrical Engineering, Yanshan University, Qinhuangdao, 066004 China Yinggan Tang, Key Lab of Industrial Computer Control Engineering of Hebei Province, Institute of Electrical Engineering, Yanshan University, Qinhuangdao, 066004 China Qing Gao, Key Lab of Industrial Computer Control Engineering of Hebei Province, Institute of Electrical Engineering, Yanshan University, Qinhuangdao, 066004 China Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    The behavior of systems of coupled nonlinear oscillators and, connected with it, the synchronization phenomena are of significant interest in many areas of science. One of the most important problems in this field is the stability of the synchronous state. The most often applied tool which allows one to quantify this stability is the largest Transversal Lyapunov Exponent (TLE) and, connected with it, Master Stability Function (MSF) theory (Pecora and Carroll in Phys. Rev. Lett. 80:2109, 1998 ). Thus there is still need to elaborate fast and simple methods of TLE calculation. The new method of the TLE estimation is presented in this paper. It applies the perturbation vector and its derivative Dot Product to calculate the largest Lyapunov exponent in the direction transversal to the synchronization manifold. The method (TLEVDP) of the TLE calculation is very simple in its background and numerical application. It does not require calculations of the Jacobi matrix eigenvalues and orthonormalization in each integration step. Thus it is fast and simple. Used methodology applies the method of Master Stability Function proposed by Pecora and Carroll (in Phys. Rev. Lett. 80:2109, 1998 ) which is undependable on the system type. Moreover on the base of the one MSF calculation one can predict complete synchronization of the sets of oscillators coupled in any coupling scheme. The theoretical improvement of the method is introduced. Results of the numerical simulations are shown and compared with other publications. Investigations of the system of Duffing oscillators coupled in ring scheme as well as the coupled Van der Pol oscillators made with use of the (TLEVDP) method are presented. Fast stabilization of the TLE value was shown. Content Type Journal Article Category Original Paper Pages 1-11 DOI 10.1007/s11071-012-0342-1 Authors Artur Dabrowski, Division of Dynamics, Technical University of Lodz, ul. Stefanowskiego 1/15, Lodz, Poland Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    A paper, “Existence of attractor and control of a 3D differential system,” was published in the journal Nonlinear Dynamics . The author tries to prove the existence of horseshoe chaos by means of the Shilnikov criterion. To do that, he uses the undetermined coefficient method to analytically demonstrate the existence of heteroclinic orbits in a Lorenz-like system. Unfortunately, his proof is not correct for two reasons. Firstly, he considers an odd function to represent the heteroclinic orbit whereas such an orbit joining two saddle-focus equilibria can never have that symmetry. Secondly, he looks for a structurally unstable Shilnikov heteroclinic orbit by means of uniformly convergent series expansions: This would imply that the dynamical object found is structurally stable. Content Type Journal Article Category Commentary Pages 1-3 DOI 10.1007/s11071-012-0407-1 Authors Antonio Algaba, Dept. Mathematics, Fac. Ciencias Experimentales, Univ. Huelva, Avda. Tres de Marzo s/n, 21071 Huelva, Spain Fernando Fernández-Sánchez, Dept. Applied Mathematics II, E.S. Ingenieros, Univ. Sevilla, Camino de los Descubrimientos s/n, 41092 Sevilla, Spain Manuel Merino, Dept. Mathematics, Fac. Ciencias Experimentales, Univ. Huelva, Avda. Tres de Marzo s/n, 21071 Huelva, Spain Alejandro J. Rodríguez-Luis, Dept. Applied Mathematics II, E.S. Ingenieros, Univ. Sevilla, Camino de los Descubrimientos s/n, 41092 Sevilla, Spain Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    This paper is concerned with the stabilization control for the offshore steel jacket platforms subject to wave-induced force. Two state feedback stabilization control schemes are proposed to reduce the vibration amplitudes of the systems. One scheme is that for the systems without actuator time-delay, a state feedback controller is designed. Compared with the nonlinear controller, both the control force and the vibration amplitudes of the systems under the state feedback controller are much reduced; and compared with the dynamic output feedback controller and the integral sliding mode controller, the required control force under the state feedback controller are significantly reduced. The other scheme is that based on the integral inequality approach, a delay-dependent state feedback controller, which can be solved by using the cone complementarity algorithm, is developed to control the systems with actuator time-delays. Compared with the state feedback controller, the delay-dependent state feedback controller is less conservative with actuator time-delays. In addition, it is capable of improving the control performance of the offshore platforms significantly, which are illustrated by simulation results. Content Type Journal Article Category Original Paper Pages 1-11 DOI 10.1007/s11071-012-0559-z Authors Bao-Lin Zhang, College of Science, China Jiliang University, Hangzhou, Zhejiang 310018, P.R. China Yue-Hua Hu, College of Science, China Jiliang University, Hangzhou, Zhejiang 310018, P.R. China Gong-You Tang, College of Information Science and Engineering, Ocean University of China, Qingdao, 266100 P.R. China Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    In this paper, using the local coordinate moving frame approach, we investigate bifurcations of generic heteroclinic loop with a hyperbolic equilibrium and a nonhyperbolic equilibrium which undergoes a pitchfork bifurcation. Under some generic hypotheses, the existence of homoclinic loop, heteroclinic loop, periodic orbit and three or four heteroclinic orbits is obtained. In addition, the non-coexistence conditions for homoclinic loop and periodic orbit are also given. Note that the results achieved here can be extended to higher dimensional systems. Content Type Journal Article Category Original Paper Pages 1-11 DOI 10.1007/s11071-012-0563-3 Authors Fengjie Geng, College of Mathematics and Science, China University of Geosciences (Beijing), Beijing, 100083 China Yancong Xu, Department of Mathematics, Hangzhou Normal University, Hangzhou, 310036 China Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    Inspirited by Li and Jin (Nonlinear Dyn. 67:2857–2864 2012 ), this paper investigates the Hopf bifurcation of a four-dimensional hyperchaotic system with only one equilibrium. A detailed set of conditions are derived, which guarantee the existence of the Hopf bifurcation. Furthermore, the standard normal form theory is applied to determine the direction and type of the Hopf bifurcation, and the approximate expressions of bifurcating periodic solutions and their periods. In addition, numerical simulations are used to justify theoretical results. Content Type Journal Article Category Original Paper Pages 1-8 DOI 10.1007/s11071-012-0536-6 Authors Hongwei Li, School of Science, Linyi University, Linyi, 276005 Shandong, China Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    Theory of marginally unstable stochastic systems, recently developed for linear systems with lumped parameters, is applied here to a nonlinear single-degree-of-freedom system. The name “marginal instability” is used for nominally stable systems with potential short-term instability due to temporal random variations of parameter(s) with brief excursions out of the stability domain. Prediction of the corresponding brief outbreaks in response is based on parabolic approximation of the parameter variation during excursion (asymptotic analysis of the Slepian model). The theory provides probabilistic description of the response (such as response probability density function (PDF) or solution to the first-passage problem) in terms of that of the parameter(s) variations. Systems with nonlinear restoring forces are considered in this Note with the use of quasiconservative version of averaging over response period. Presented results illustrate influence of nonlinearities on the response characteristics which are important for reliability evaluation. Content Type Journal Article Category Original Paper Pages 1-5 DOI 10.1007/s11071-012-0570-4 Authors M. F. Dimentberg, Mechanical Engineering Department, Worcester Polytechnic Institute, 100 Institute Road, Worcester, MA 01609, USA Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    In this paper, higher order frequency response functions, based on the Volterra series, are employed to characterise the input-output behaviour of the non-linear viscous Burgers’ equation subject to sinusoidal excitation. First, a formal Volterra series representation for each spatial location is derived for the solution of Burgers’ equation with a boundary condition as the input to the system. Then a systematic method is presented to obtain the higher order frequency kernels of the Volterra series at each spatial location by solving a series of ordinary differential equations. It is shown that the convergence region of the individual harmonics with respect to the magnitude of the input excitation can be estimated by using these higher order kernels. The frequency characteristics of Burgers’ equation is investigated and compared with numerical simulation. Content Type Journal Article Category Original Paper Pages 1-13 DOI 10.1007/s11071-012-0571-3 Authors L. Z. Guo, Department of Automatic Control and Systems Engineering, The University of Sheffield, Sheffield, S1 3JD UK Y. Z. Guo, Department of Automatic Control and Systems Engineering, The University of Sheffield, Sheffield, S1 3JD UK S. A. Billings, Department of Automatic Control and Systems Engineering, The University of Sheffield, Sheffield, S1 3JD UK D. Coca, Department of Automatic Control and Systems Engineering, The University of Sheffield, Sheffield, S1 3JD UK Z. Q. Lang, Department of Automatic Control and Systems Engineering, The University of Sheffield, Sheffield, S1 3JD UK Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    Steady-state free vibrations, with large amplitude displacements, of variable stiffness composite laminated plates (VSCL) are analysed. The intentions of this research are: (1) to find out how the natural frequencies and (mode) shapes evolve with the displacement amplitude in this new type of laminated composite material; (2) to describe modal interactions in VSCL due to energy interchanges under the coupling induced by non-linearity; (3) to compare the VSCL with traditional, constant stiffness, laminated plates. The VSCL of interest here have curvilinear fibres and the numerical analysis carried out is based on a recently developed p -version finite element with hierarchic basis functions. The element follows first-order shear deformation theory and considers Von Kármán’s non-linear terms. The time domain equations of motion are first reduced using the linear modes of vibration and then transformed to the frequency domain via the harmonic balance method. These frequency domain equations are solved by an arc-length continuation method. Content Type Journal Article Category Original Paper Pages 1-14 DOI 10.1007/s11071-012-0554-4 Authors Pedro Ribeiro, DEMec/IDMEC, Faculdade de Engenharia, Universidade do Porto, rua Dr. Roberto Frias, s/n, 4200-465 Porto, Portugal Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    In this paper, an adaptive impulse control with only one restriction criterion is derived to achieve synchronization of nonlinear chaotic systems in the exponential rate of convergence. It is assumed that the system satisfies the local Lipschitz condition and the Lipschitz constant is estimated by an augmented adaptation equation. The significance of the related control parameters in the criterion is also discussed in detail. The Duffing and the Lorenz systems have been simulated to illustrate the theoretical analysis. Content Type Journal Article Category Original Paper Pages 1-9 DOI 10.1007/s11071-012-0574-0 Authors Yen-Sheng Chen, Institute of Applied Mechanics, National Taiwan University, Taipei, 106 Taiwan, ROC Chien-Cheng Chang, Institute of Applied Mechanics, National Taiwan University, Taipei, 106 Taiwan, ROC Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    A mathematical model is developed to investigate the grazing dynamics of tapping mode atomic force microscopes (AFM) subjected to a base harmonic excitation. A multimode Galerkin approximation is utilized to discretize the nonlinear partial differential equation of motion governing the cantilever response and associated boundary conditions and obtain a set of nonlinearly coupled ordinary differential equations governing the time evolution of the system dynamics. A comprehensive numerical analysis is performed for a wide range of the excitation amplitude and frequency. The tip oscillations are examined using nonlinear dynamic tools through several examples. The non-smoothness in the tip/sample interaction model is treated rigorously. A higher-mode Galerkin analysis indicates that period doubling bifurcations and chaotic vibrations are possible in tapping mode microscopy for certain operating parameters. It is also found that a single-mode Galerkin approximation, which accurately predicts the tip nonlinear responses far from the sample, is not adequate for predicting all of the nonlinear phenomena exhibited by an AFM, such as grazing bifurcations, and leads to both quantitative and qualitative errors. Content Type Journal Article Category Original Paper Pages 1-13 DOI 10.1007/s11071-012-0560-6 Authors Arash Bahrami, Department of Engineering Science and Mechanics, Virginia Polytechnic Institute and State University, MC 0219, Blacksburg, VA 24061, USA Ali H. Nayfeh, Department of Engineering Science and Mechanics, Virginia Polytechnic Institute and State University, MC 0219, Blacksburg, VA 24061, USA Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    We develop and investigate a mathematical model of an aircraft nose landing gear with a dual-wheel configuration. The main aim here is to study the influence of a dual-wheel configuration on the existence of shimmy oscillations. To this end, we consider a model that describes the torsional and lateral vibrational modes and the non-linear interaction between them via the tyre-ground contact. More specifically, we perform a bifurcation analysis (with the software package auto ) of the model in the two-parameter plane of forward velocity of the aircraft and vertical load on the nose landing gear. This two-parameter bifurcation diagram allows one to identify regions of different dynamics, and the question addressed here is how it depends on two key parameters of the dual-wheel configuration. Namely, we consider the influence of, first, the separation distance between the two wheels and, second, of gyroscopic effects arising from the inertia of the wheels. For both cases, we find that with increasing separation distance and wheel inertia, respectively, the lateral mode becomes more stable and the torsional mode becomes less stable. More specifically, we present associated bifurcation scenarios that explain the transitions between qualitatively different two-parameter bifurcation diagrams. Overall, we find that the separation distance and gyroscopic effects due to wheel inertia may have a significant influence on the quantitative and qualitative nature of shimmy oscillations in aircraft nose landing gears. In particular, the torsional and the lateral modes of a dual-wheel nose landing gear may interact in a quite complicated fashion. Content Type Journal Article Category Original Paper Pages 1-14 DOI 10.1007/s11071-012-0565-1 Authors Phanikrishna Thota, Airbus, Filton, Bristol, BS99 7AR UK Bernd Krauskopf, Department of Engineering Mathematics, University of Bristol, University Walk, Bristol, BS8 1TR UK Mark Lowenberg, Department of Aerospace Engineering, University of Bristol, University Walk, Bristol, BS8 1TR UK Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    A new method of stabilizing low-order, proper orthogonal decomposition based reduced-order models of the Navier–Stokes equations is proposed. Unlike traditional approaches, this method does not rely on empirical turbulence modeling or modification of the Navier–Stokes equations. It provides spatial basis functions different from the usual proper orthogonal decomposition basis function in that, in addition to optimally representing the solution, the new proposed basis functions also provide stable reduced-order models. The proposed approach is illustrated with two test cases: two-dimensional flow inside a square lid-driven cavity and a two-dimensional mixing layer. Content Type Journal Article Category Original Paper Pages 1-14 DOI 10.1007/s11071-012-0561-5 Authors Maciej Balajewicz, Mechanical Engineering and Materials Science, Duke University, Durham, NC 27708-0300, USA Earl H. Dowell, Mechanical Engineering and Materials Science, Duke University, Durham, NC 27708-0300, USA Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    Synchronization between uncertain chaotic systems with a diverse structure is investigated using a second-order sliding mode control. Sliding surface, adaptive laws of the unknown parameters, and the sliding mode controller are designed based on stability theory. The Van der Pol system with chaotic behavior in physics is taken as a target system; the Duffing system with unknown parameters is taken as a response system. The artificial simulation results show that this method is still effective. Content Type Journal Article Category Original Paper Pages 1-5 DOI 10.1007/s11071-012-0578-9 Authors Ling Lü, College of Physics and Electronic Technology, Liaoning Normal University, Dalian, 116029 China Miao Yu, College of Physics and Electronic Technology, Liaoning Normal University, Dalian, 116029 China Ling Luan, Physical Science and Technology Institute, Dalian University, Dalian, 116622 China Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    Lyapunov exponents indicate the asymptotic behaviors of nonlinear systems, the concept of which is a powerful tool of the stability analysis for nonlinear systems, especially when the dynamic models of the systems are available. For real world systems, however, such models are often unknown, and estimating the exponents reliably from experimental data is notoriously difficult. In this paper, a novel method of estimating Lyapunov exponents from a time series is presented. The method combines the ideas of reconstructing the attractor of the system under study and approximating the embedded attractor through tuning a Radial-Basis-Function (RBF) network, based on which the Jacobian matrices can be easily derived, making the model-based algorithm applicable. Three case studies are presented to demonstrate the efficacy of the proposed method. The Hénon map and the Lorenz system feature spectra including not only the positive exponent, but also the negative one, while the standing biped balance system is characterized by four negative exponents. Compared with the existing methods, the numerical accuracy of the Lyapunov exponents derived through the newly proposed method is much higher regardless of their signs even in the presence of measurement noise. We believe that the work can contribute to the stability analysis of nonlinear systems of which the dynamics are either unknown or difficult to model due to complexities. Content Type Journal Article Category Original Paper Pages 1-20 DOI 10.1007/s11071-012-0567-z Authors Yuming Sun, Department of Mechanical and Manufacturing Engineering, University of Manitoba, Winnipeg, Canada Christine Qiong Wu, Department of Mechanical and Manufacturing Engineering, University of Manitoba, Winnipeg, Canada Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    The dynamic analysis of a cracked rotor with a breathing crack leads to the formulation of a nonlinear time-dependent problem. For the simple Jeffcott rotor model, this problem has been addressed using numerical integration methods that are very time consuming. A first simplification can be done assuming that the stiffness is a time-dependent function obtained with the quasi-static displacements of the shaft. In this study, we propose a new procedure to analyze the nonlinear dynamic of such a kind of cracked rotors using an iterative technique that transforms the full nonlinear problem in a succession of time-dependent linear ones. We show with different examples that this technique virtually gives the same results as the classical integration methods, but being much more efficient and achieving a significant saving of computation time. The calculations using the proposed method are over a 100 times faster than the corresponding to integrate the full nonlinear problem, being very helpful in on-line crack identification procedures. Also, this analysis shows that, in cases for which the vertical whirl amplitude is greater than the shaft weight static deflection, the use of simplified methods based on the quasi-static stiffness matrix could not be adequate. Content Type Journal Article Category Original Paper Pages 1-15 DOI 10.1007/s11071-012-0569-x Authors L. Rubio, Department of Mechanical Engineering, University Carlos III, Madrid, Spain J. Fernández-Sáez, Department of Continuum Mechanics and Structural Analysis, University Carlos III, Madrid, Spain Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    We study the effects of a dichotomous periodic force on meandering and rigidly rotating spiral waves. For a meandering state, the periodic forcing induces more modulating frequencies according to the rules of frequency-locked relations and linear combinations. It can also generate some unique closed tip orbits. On the modulating period T -axis, there exist all kinds of resonant entrainment bands. Arnold tongues exist in the period-amplitude space. The width of entrainment bands is affected by the symmetry of positive and negative parts in each signal unit. In addition, appropriate choices of T -value can be used to eliminate spiral waves. For a rigidly rotating state, the periodic forcing can induce a transition toward meandering spiral waves via generating a transitive bidirectional spiral wave. It is very interesting that, after the transition, the meandering spiral wave has the same primary rotating period as the free meandering states. Content Type Journal Article Category Original Paper Pages 1-12 DOI 10.1007/s11071-012-0568-y Authors Guoyong Yuan, Department of Physics, Hebei Normal University, Shijiazhuang, 050024 China Yaping Liu, Department of Physics, Hebei Normal University, Shijiazhuang, 050024 China Aiguo Xu, Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing, 100088 China Guangrui Wang, Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing, 100088 China Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    This paper studies systematically a Bedd-ington–DeAngelis prey–predator system with harvesting and impulsive state feedback control. Conditions for existence and stability of predator-free periodic solution are obtained. When the predator-free periodic solution loses its stability, the existence and stability of nontrivial period solution are also established. Furthermore, computer simulations show that this impulsive system displays a series of complex phenomena, including period-doubling bifurcation and cascade, period window, and chaotic bands. Through numerical simulation, it is also observed that capture capability can influence the amount of predator released and the interval of the stability for nontrivial period-1 solution. Moreover, the superiority of impulsive state feedback control strategy is also exhibited over the impulsive fixed-time control. Content Type Journal Article Category Original Paper Pages 1-12 DOI 10.1007/s11071-012-0551-7 Authors Yi Zhang, Institute of Systems Science, Northeastern University, Shenyang, 110819 P.R. China Qingling Zhang, Institute of Systems Science, Northeastern University, Shenyang, 110819 P.R. China Xue Zhang, Institute of Systems Science, Northeastern University, Shenyang, 110819 P.R. China Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    In this paper, we focus on the synchronization between integer-order chaotic systems and a class of fractional-order chaotic system using the stability theory of fractional-order systems. A new fuzzy sliding mode method is proposed to accomplish this end for different initial conditions and number of dimensions. Furthermore, three examples are presented to illustrate the effectiveness of the proposed scheme, which are the synchronization between a fractional-order Lü chaotic system and an integer-order Liu chaotic system, the synchronization between a fractional-order hyperchaotic system based on Chen’s system and an integer-order hyperchaotic system based upon the Lorenz system, and the synchronization between a fractional-order hyperchaotic system based on Chen’s system, and an integer-order Liu chaotic system. Finally, numerical results are presented and are in agreement with theoretical analysis. Content Type Journal Article Category Original Paper Pages 1-13 DOI 10.1007/s11071-012-0555-3 Authors Diyi Chen, Department of Electrical Engineering, Northwest A&F University, Yangling, Shaanxi 712100, P.R. China Runfan Zhang, Department of Electrical Engineering, Northwest A&F University, Yangling, Shaanxi 712100, P.R. China Julien Clinton Sprott, Department of Physics, University of Wisconsin, Madison, WI 53706, USA Xiaoyi Ma, Department of Electrical Engineering, Northwest A&F University, Yangling, Shaanxi 712100, P.R. China Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    By introducing a suitable change of variable theorem for a class of fractional discontinuous equations, we study the possibility to use a periodic perturbation algorithm to stabilize chaotic trajectories. For this purpose, some new issues of fractional differential inclusions and results on Filippov systems are used. The algorithm, which periodically changes the system variables, has been used so far to stabilize discrete, continuous and discontinuous systems of integer order. As an example, a piece-wise continuous variant of the Chen system is utilized. Content Type Journal Article Category Original Paper Pages 1-9 DOI 10.1007/s11071-012-0497-9 Authors Marius-F. Danca, Dept. of Mathematics and Computer Science, Avram Iancu University, 400380 Cluj-Napoca, Romania Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    This paper studies the dynamics of shallow water waves that are governed by the Boussinesq equations. A few perturbation terms are taken into account. The ansatz method is used to carry out the perturbed Boussinesq equation. Later on, the mapping method is used to extract a few more analytical solutions. Additionally, the Weierstrass elliptic function method is also used to obtain solitary waves and singular soliton solutions. Finally, the Lie symmetry approach is used to extract a few more additional solutions. Content Type Journal Article Category Original Paper Pages 1-9 DOI 10.1007/s11071-012-0525-9 Authors E. V. Krishnan, Department of Mathematics and Statistics, Sultan Qaboos University, P.O. Box 36, Al Khod 123, Muscat, Oman Sachin Kumar, School of Mathematics and Computer Applications, Thapar University, Patiala, 147004 Punjab, India Anjan Biswas, Department of Mathematical Sciences, Delaware State University, Dover, DE 19901-2277, USA Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    In 1695, G. Leibniz laid the foundations of fractional calculus, but mathematicians revived it only 300 years later. In 1971, L.O. Chua postulated the existence of a fourth circuit element, called memristor , but Williams’s group of HP Labs realized it only 37 years later. By looking at these interdisciplinary and promising research areas, in this paper, a novel fractional-order system including a memristor is introduced. In particular, chaotic behaviors in the simplest fractional-order memristor-based system are shown. Numerical integrations (via a predictor–corrector method) and stability analysis of the system equilibria are carried out, with the aim to show that chaos can be found when the order of the derivative is 0.965. Finally, the presence of chaos is confirmed by the application of the recently introduced 0-1 test . Content Type Journal Article Category Original Paper Pages 1-13 DOI 10.1007/s11071-012-0522-z Authors Donato Cafagna, Dipartimento Ingegneria Innovazione, Università del Salento, Lecce, Italy Giuseppe Grassi, Dipartimento Ingegneria Innovazione, Università del Salento, Lecce, Italy Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    This work aims at the preparation of an experiment for the thermal modeling of an ARMCO iron sample (iron of the American Rolling Mill COmpany) for small temperature variations around different operating points. Fractional models have proven their efficacy for modeling thermal diffusion around the ambient temperature and for small variations. Due to their compactness, as compared to rational models and to finite element models, they are suitable for modeling such diffusive phenomena. However, for large temperature variations, thermal characteristics such as thermal conductivity and specific heat vary along with the temperature. In this context, the thermal diffusion obeys a nonlinear partial differential equation and cannot be modeled by a single linear model. In this paper, thermal diffusion of the iron sample is modeled around different operating points for temperatures ranging from 400 to 1070 K, which is above the Curie point (In physics and materials science, the Curie temperature ( T C ), or Curie point, is the temperature at which a ferromagnetic or a ferrimagnetic material becomes paramagnetic.) showing that for a large range of temperature variations, a nonlinear model is required. Identification and validation data are generated by finite element methods using COMSOL Software. Content Type Journal Article Category Review Pages 1-10 DOI 10.1007/s11071-012-0507-y Authors Asma Maachou, IPB/ENSEIRB-MATMECA, IMS UMR 5218 CNRS, Université Bordeaux 1, 351 cours de la Libération, Bât A4, 33405 Talence Cedex, France Rachid Malti, IPB/ENSEIRB-MATMECA, IMS UMR 5218 CNRS, Université Bordeaux 1, 351 cours de la Libération, Bât A4, 33405 Talence Cedex, France Pierre Melchior, IPB/ENSEIRB-MATMECA, IMS UMR 5218 CNRS, Université Bordeaux 1, 351 cours de la Libération, Bât A4, 33405 Talence Cedex, France Jean-Luc Battaglia, ENSAM, TREFLE UMR 8508 CNRS, Esplanade des Arts et Metiers, Université de Bordeaux 1, 33405 Talence Cedex, France Bruno Hay, LNE, Centre Metrologie et Instrumentation, 29 avenue Roger Hennequin, 78197 Trappes Cedex, France Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    The power law wave equation uses two different fractional derivative terms to model wave propagation with power law attenuation. This equation averages complex nonlinear dynamics into a convenient, tractable form with an explicit analytical solution. This paper develops a random walk model to explain the appearance and meaning of the fractional derivative terms in that equation, and discusses an application to medical ultrasound. In the process, a new strictly causal solution to this fractional wave equation is developed. Content Type Journal Article Category Original Paper Pages 1-9 DOI 10.1007/s11071-012-0532-x Authors Mark M. Meerschaert, Department of Statistics and Probability, Michigan State University, East Lansing, MI 48824, USA Peter Straka, Department of Statistics and Probability, Michigan State University, East Lansing, MI 48824, USA Yuzhen Zhou, Department of Statistics and Probability, Michigan State University, East Lansing, MI 48824, USA Robert J. McGough, Department of Electrical and Computer Engineering, Michigan State University, East Lansing, MI 48824, USA Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    In this paper, the Nonlinear Normal Modes ( NNMs ) analysis for the case of three-to-one (3:1) internal resonance of a slender simply supported beam in presence of compressive axial load resting on a nonlinear elastic foundation is studied. Using the Euler–Bernoulli beam model, the governing nonlinear PDE of the beam’s transverse vibration and also its associated boundary conditions are extracted. These nonlinear motion equation and boundary condition relations are solved simultaneously using four different approximate-analytical solution techniques, namely the method of Multiple Time Scales , the method of Normal Forms , the method of Shaw and Pierre , and the method of King and Vakakis . The obtained results at this stage using four different methods which are all in time–space domain are compared and it is concluded that all the methods result in a similar answer for the amplitude part of the transverse vibration. At the next step, the nonlinear normal modes are obtained. Furthermore, the effect of axial compressive force in the dynamic analysis of such a beam is studied. Finally, under three-to-one-internal resonance condition the NNMs of the beam and the steady-state stability analysis are performed. Then the effect of changing the values of different parameters on the beam’s dynamic response is also considered. Moreover, 3-D plots of stability analysis in the steady-state condition and the beam’s amplitude frequency response curves are presented. Content Type Journal Article Category Original Paper Pages 1-26 DOI 10.1007/s11071-012-0520-1 Authors Ahmad Mamandi, Department of Mechanical Engineering, Parand Branch, Islamic Azad University, Tehran, Iran Mohammad H. Kargarnovin, Department of Mechanical Engineering, Sharif University of Technology, Tehran, Iran Salman Farsi, Department of Mechanical Engineering, Tarbiat Modares University, Tehran, Iran Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    This paper presents a periodically driven Rayleigh–Duffing-like system with the function x | x |. It is proven via the Melnikov function method that the quadratic function x | x | induces Smale horseshoes to the Rayleigh–Duffing-like system. The Rayleigh–Duffing-like oscillator with fractional order is also discussed, and results of computer simulation demonstrate the chaotic dynamic behaviors of the system. Furthermore, two fractional Rayleigh–Duffing-like systems are synchronized by active control technology, the method based on state observer and nonlinear feedback method. Numerical results validate the effectiveness and applicability of the proposed synchronization schemes. Content Type Journal Article Category Original Paper Pages 1-11 DOI 10.1007/s11071-012-0521-0 Authors Yan-Lan Zhang, Department of Computer Sciences and Engineering, Zhangzhou Normal University, Zhang’zhou, Fu’jian 363000, P.R. China Mao-Kang Luo, College of Mathematics, Sichuan University, Cheng’du, Si’chuan 610064, P.R. China Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    In this paper, we study Hopf-zero bifurcation in a generalized Gopalsamy neural network model. By using multiple time scales and center manifold reduction methods, we obtain the normal forms near a Hopf-zero critical point. A comparison between these two methods shows that the two normal forms are equivalent. Moreover, bifurcations are classified in two-dimensional parameter space near the critical point, and numerical simulations are presented to demonstrate the applicability of the theoretical results. Content Type Journal Article Category Original Paper Pages 1-14 DOI 10.1007/s11071-012-0511-2 Authors Yuting Ding, Department of Mathematics, Harbin Institute of Technology, Harbin, 150001 China Weihua Jiang, Department of Mathematics, Harbin Institute of Technology, Harbin, 150001 China Pei Yu, Department of Applied Mathematics, The University of Western Ontario, London, Ontario N6A 5B7, Canada Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    A new anticipation driving car-following (AD-CF) model is presented based on the effect of traffic anticipation in the real world. The model’s linear stability condition was obtained by applying the linear stability theory. Additionally, a modified Korteweg–de Vries (mKdV) equation was derived via nonlinear analysis to describe the propagating behavior of traffic density wave near the critical point. Good agreement between the simulation and the analytical results shows that the stability of traffic flow can be enhanced when the driver’s anticipation effects are considered. Content Type Journal Article Category Original Paper Pages 1-7 DOI 10.1007/s11071-012-0524-x Authors Lin-Jiang Zheng, Key Laboratory of Dependable Service Computing in Cyber Physical Society (Chongqing University), Ministry of Education, Chongqing, 400030 China Chuan Tian, Key Laboratory of Dependable Service Computing in Cyber Physical Society (Chongqing University), Ministry of Education, Chongqing, 400030 China Di-Hua Sun, Key Laboratory of Dependable Service Computing in Cyber Physical Society (Chongqing University), Ministry of Education, Chongqing, 400030 China Wei-Ning Liu, Key Laboratory of Dependable Service Computing in Cyber Physical Society (Chongqing University), Ministry of Education, Chongqing, 400030 China Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    The problem of global asymptotical synchronization of chaotic Lur’e systems using sampled-data controller is considered in this paper. Sufficient conditions are obtained in terms of effective synchronization linear matrix inequality using a piecewise sawtooth structure of the sampling in time by constructing the new discontinuous Lyapunov functionals. The sampled-data feedback control gain is obtained from the derived condition. The Chua system and horizontal platform system are taken for numerical demonstration to show the effectiveness of the proposed condition. Content Type Journal Article Category Original Paper Pages 1-11 DOI 10.1007/s11071-012-0590-0 Authors S. Jeeva Sathya Theesar, Department of Mathematics, Gandhigram Rural Institute—Deemed University, Gandhigram, 624302 Tamil Nadu, India Santo Banerjee, Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia P. Balasubramaniam, Department of Mathematics, Gandhigram Rural Institute—Deemed University, Gandhigram, 624302 Tamil Nadu, India Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    In this paper, via the Painlevé analysis and multi-linear variable separation, the (2+1)-dimensional variable-coefficient breaking soliton model in certain fluids and plasmas is investigated, with the Bäcklund transformation and analytic solutions presented explicitly. With those solutions, four kinds of the localized solitonic excitations are obtained, as the multi-shock-lump, multi-instanton, saddle-type-multiple-ring-soliton, and single-loop- breather structures. Figures indicate that the shapes, velocities, and propagation paths of those four kinds are affected by the variable coefficients, yielding the dynamic features, elastic interactions, parallel propagations, and periodic propagation of the analytic bound localized solitonic excitations. Content Type Journal Article Category Original Paper Pages 1-13 DOI 10.1007/s11071-012-0581-1 Authors Fu-Wei Sun, Ministry-of-Education Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics, Beijing, 100191 China Jiu-Xian Cai, College of Science, North China University of Technology, Beijing, 100144 China Yi-Tian Gao, Ministry-of-Education Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics, Beijing, 100191 China Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    This paper proposes a near optimal controller design method for unified chaotic systems based on state-dependent Riccati equation (SDRE) approach. A parameterization of the optimal nonlinear control gain is given in terms of the solution matrix of an SDRE. A simple algorithm to compute the near optimal control gain is proposed. The proposed near optimal control design method is also extended to the synchronization problem for unified chaotic systems. Finally, the effectiveness of the proposed design method is verified via numerical simulations. Content Type Journal Article Category Original Paper Pages 1-8 DOI 10.1007/s11071-012-0598-5 Authors Han Ho Choi, Division of EEE, Dongguk Univ.-Seoul, 26, 3-ga, Pil-dong, Chung-gu, Seoul, 100-715 Korea Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    In this paper, we study the stability of a mathematical model for trajectory generation of a qua-druped robot. We consider that each movement is composed of two types of primitives: rhythmic and discrete. The discrete primitive is inserted as a perturbation of the purely rhythmic movement. The two primitives are modeled by nonlinear dynamical systems. We adapt the theory developed by Golubitsky et al. in (Physica D 115: 56–72, 1998 ; Buono and Golubitsky in J. Math. Biol. 42:291–326, 2001 ) for quadrupeds gaits. We conclude that if the discrete part is inserted in all limbs, with equal values, and as an offset of the rhythmic part, the obtained gait is stable and has the same spatial and spatiotemporal symmetry groups as the purely rhythmic gait, differing only on the value of the offset. Content Type Journal Article Category Original Paper Pages 1-6 DOI 10.1007/s11071-012-0600-2 Authors Carla M. A. Pinto, Centro de Matemática da Universidade do Porto, Rua Dr António Bernardino de Almeida, 431, 4200-072 Porto, Portugal Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    An aeroelastic system is a nonlinear system with two freedoms, i.e., the plunge displacement and the pitch angle, in a dynamic system model. A chaos effect or a limit cycle oscillation is presumably attributed to the nonlinear effect of the pitch angle mentioned above or the interaction between the aerodynamic behaviors. It is that a single trailing edge input in an aeroelastic system is employed as a way to suppress the limit cycle oscillation with an exclusive choice between the plunge displacement and the pitch angle for a control law design. Consequently, the remaining inevitably turns into an internal dynamics, whose stability is adversely affected by the flight speed and structure parameters, a problem improved by no means using a singe control input design. Toward this end, this work presents a controller design criterion with multiple input channels for both the leading and training edges to remove the uncertainty effect of internal dynamics, and render more room for the response design of the plunge displacement as well as the pitch angle. Mostly due to external disturbance and unknown uncertainty, there is a deviation between the intended and implemented system performances for a robust control design, a mainstream research issue in the modern control. As a consequence of a sliding mode control utilized here, the limit cycle oscillation suffered in an aeroelastic system is removed effectively by the use of a terminal sliding mode control, and the chattering phenomenon seen in the control signal is hence eliminated by his method. It is seen from simulations that the control system is stably assured to reach the target within a limited time frame with an addition of a saturation function to the control law. Content Type Journal Article Category Original Paper Pages 1-12 DOI 10.1007/s11071-012-0593-x Authors Chieh-Li Chen, Department of Aeronautics and Astronautics, National Cheng Kung University, Tainan, Taiwan Chung-Wei Chang, Department of Aeronautics and Astronautics, National Cheng Kung University, Tainan, Taiwan Her-Terng Yau, Department of Electrical Engineering, National Chin-Yi University of Technology, Taichung, Taiwan Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    Critical conditions of period-doubling bifurcation and saddle-node bifurcation are derived for a class of switched linear systems. They can be applied to other similar hybrid, Filippov, or piecewise-smooth systems. Such switched linear systems are common in DC-DC converters. Those previously known critical conditions in the past research become special cases in the generalized framework. Given an arbitrary control scheme, a systematic procedure is proposed to derive the critical condition, which shows the stable range of a system parameter and the minimum stabilizing ramp slope. Two different systems with similar loop gains at high frequency have similar forms of critical conditions. The effect of switching delay is also analyzed. Content Type Journal Article Category Original Paper Pages 1-23 DOI 10.1007/s11071-012-0572-2 Authors Chung-Chieh Fang, Advanced Analog Technology, 2F, No. 17, Industry E. 2nd Rd., Hsinchu, 300 Taiwan Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    Based on previous studies, a new spatial curved slender-beam finite element and a new cylindrical shell finite element are proposed in the frame of gradient-deficient Absolute Nodal Coordinate Formulation (ANCF). The strain energy of the beam element is derived by using the definition of the Green–Lagrange strain tensor in continuum mechanics so that the assumption on small strain can be relaxed. By using the differential geometry and the continuum mechanics, the angle between two base vectors of a defined local coordinate frame of the cylindrical shell element is introduced into the strain energy formulations. Therefore, the new shell element can be used to model parallelogram shells. The analytical formulations of elastic forces and their Jacobian for the above two finite elements of gradient-deficient ANCF are also derived via the skills of tensor analysis. The generalized-alpha method is used to solve the huge set of system equations. Finally, four case studies including both static and dynamic problems are given to validate the proposed beam and cylindrical shell elements of gradient-deficient ANCF. Content Type Journal Article Category Original Paper Pages 1-16 DOI 10.1007/s11071-012-0582-0 Authors Cheng Liu, MOE Key Laboratory of Dynamics and Control of Flight Vehicle, School of Aerospace Engineering, Beijing Institute of Technology, Beijing, 100081 China Qiang Tian, MOE Key Laboratory of Dynamics and Control of Flight Vehicle, School of Aerospace Engineering, Beijing Institute of Technology, Beijing, 100081 China Haiyan Hu, MOE Key Laboratory of Dynamics and Control of Flight Vehicle, School of Aerospace Engineering, Beijing Institute of Technology, Beijing, 100081 China Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    Decentralized control is the most favorite control of robot manipulators due to computational simplicity and ease of implementation. Beside that, adaptive fuzzy control efficiently controls uncertain nonlinear systems. These motivate us to design a decentralized fuzzy controller. However, there are some challenging problems to guarantee stability. The state-space model of the robotic system including the robot manipulator and motors is in a noncompanion form, multivariable, highly nonlinear, and heavily coupled with a variable input gain matrix. For this purpose, adaptive fuzzy control may use all variable states. As a result, it suffers from computational burden. To overcome the problems, we present a novel decentralized Direct Adaptive Fuzzy Control (DAFC) of electrically driven robot manipulators using the voltage control strategy. The proposed DAFC is simple, in a decentralized structure with high-accuracy response, robust tracking performance, and guaranteed stability. Instead of all state variables, only the tracking error of every joint and its derivative are given as the inputs of the controller. The proposed DAFC is simulated on a SCARA robot driven by permanent magnet dc motors. Simulation results verify superiority of the decentralized DAFC to a decentralized PD-fuzzy controller. Content Type Journal Article Category Original Paper Pages 1-12 DOI 10.1007/s11071-012-0583-z Authors Mohammad Mehdi Fateh, Department of Electrical and Robotic Engineering, Shahrood University of Technology, University Street, 3619995161 Shahrood, Iran Sara Fateh, Department of Electrical and Robotic Engineering, Shahrood University of Technology, University Street, 3619995161 Shahrood, Iran Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung: Erratum to: Delayed-state-feedback exponential stabilization for uncertain Markovian jump systems with mode-dependent time-varying state delays Content Type Journal Article Category Erratum Pages 1-14 DOI 10.1007/s11071-012-0595-8 Authors Huabin Chen, Department of Mathematics, Nanchang University, Nanchang, 330031 Jiangxi Province, P.R. China Chuanxi Zhu, Department of Mathematics, Nanchang University, Nanchang, 330031 Jiangxi Province, P.R. China Peng Hu, School of Mathematics and Physics, China University of Geosciences, Wuhan, 430074 Hubei Province, P.R. China Yong Zhang, College of Information Science and Technology, Wuhan University of Science and Technology, Wuhan, 430081 Hubei Province, P.R. China Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    Episodic or compound bursting arises from a transition between a burst episode composed of a long burst and several short bursts and a relatively long subthreshold oscillation in this work. The minimal and generic phantom bursting model proposed by Bertram et al. is employed to produce compound bursting of a single pancreatic β -cell and compound bursting synchronization with antiphase spikes of two electrical coupling pancreatic β -cells. Two different fast/slow analysis for the moderate and the slower slow variables in three-dimensional spaces are combined to highlight better how these two slow variables with different time scales commonly or separately result in complex dynamic of the compound bursting of both the single β -cell and the two electrical coupling β -cells. For the compound bursting synchronization with antiphase spikes, we reveal how varying coupling strength leads to a change of the number of short bursts within the burst episode for different types of compound bursting. Content Type Journal Article Category Original Paper Pages 1-11 DOI 10.1007/s11071-012-0592-y Authors Zhuoqin Yang, School of Mathematics and System Sciences, Beihang University, Beijing, 100191 China Qingyun Wang, Department of Dynamics and Control, Beihang University, Beijing, 100191 China Marius-F. Danca, Department of Mathematics and Computer Science, Avram Iancu University, Cluj-Napoca, 400380 Romania Jiaoying Zhang, School of Mathematics and System Sciences, Beihang University, Beijing, 100191 China Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    In this paper, a fuzzy adaptive controller is proposed for a single-link flexible-joint robot. Fuzzy logic systems are used to approximate unknown nonlinearities, and then a fuzzy state observer is designed to estimate the immeasurable states. By combining the adaptive backstepping design with dynamic surface control (DSC) technique, a fuzzy adaptive output-feedback backstepping control approach is developed. It is proved that all the signals of the resulting closed-loop system are semiglobally uniformly ultimately bounded (SGUUB), and both the observer and tracking errors converge to a small neighborhood of the origin by appropriate choosing the design parameters. The simulation results are provided to demonstrate the effectiveness of the proposed controller. Two key advantages of our scheme are that (i) the proposed control method does not require that the link velocity and actuator velocity of single-link flexible-joint robot be measured directly, and (ii) the problem of “explosion of complexity” is avoided. Content Type Journal Article Category Original Paper Pages 1-14 DOI 10.1007/s11071-012-0596-7 Authors Yongming Li, Department of Basic Mathematics, Liaoning University of Technology, Jinzhou, Liaoning 121001, P.R. China Shaocheng Tong, Department of Basic Mathematics, Liaoning University of Technology, Jinzhou, Liaoning 121001, P.R. China Tieshan Li, Navigation College, Dalian Maritime University, Dalian, Liaoning 116026, P.R. China Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    This paper is concerned with the problem of asymptotic synchronization of a class of chaotic systems in the presence of network deterioration and time-varying delays. Based on adaptive adjustment technique and circuitry principle, a new version of the active coupling as well as its circuit realization is proposed. Then, an approach that is based on application of Lyapunov stability theory for the synchronization error system is introduced to prove the asymptotic synchronization result of the overall chaotic system. Moreover, a condition which denotes that at least one coupling will not be deteriorated for synchronization of the network is provided in the paper. It is shown that, without control inputs, the result can also be established for the deteriorated coupling networks and any time-varying bounded delay under the topological structure satisfying the condition. Finally, the proposed active couplings are physically implemented by circuits and tested by simulation on a Chua’s circuit network. Content Type Journal Article Category Original Paper Pages 1-11 DOI 10.1007/s11071-012-0579-8 Authors Xiao-Zheng Jin, Key Laboratory of Manufacturing Industrial Integrated Automation, Shenyang University, Shenyang, 110044 P.R. China Wei-Wei Che, Key Laboratory of Manufacturing Industrial Integrated Automation, Shenyang University, Shenyang, 110044 P.R. China Dan Wang, Key Laboratory of Manufacturing Industrial Integrated Automation, Shenyang University, Shenyang, 110044 P.R. China Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    In the present paper, a super-extension of the Yang hierarchy is proposed by super-matrix Lie algebras, and the super-Yang hierarchy with self-consistent sources is established. Furthermore, we establish infinitely many conservation laws of the super-integrable hierarchy. The methods presented by us can be generalized to other nonlinear equation hierarchies with self-consistent sources. Content Type Journal Article Category Original Paper Pages 1-8 DOI 10.1007/s11071-012-0585-x Authors Tiecheng Xia, Department of Mathematics, Shanghai University, Shanghai, 200444 China Temuer Chaolu, Department of Mathematics, Shanghai Maritime University, Shanghai, 200135 China Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    To prevent or mitigate the cascading propagation on complex networks more efficiently, taking into account some existing protections and measures in real-life networks, we introduce a new mitigation strategy. Applying the global removal and two attacking strategies, we demonstrate the efficiency of the mitigation method on improving the robustness level against cascading failures in Barabási–Albert (BA) scale-free networks and in the Internet, as well as in the power grid of the western United States. We show that only making simple adjustments to the overload edges can dramatically enhance the robustness of diverse networks subject to the global removal and targeted attacks. We further compare the mitigation strategy in two attacks and observe to what extent the improvement of the robustness in two attacks depends on the parameters in our cascading model. In addition, by the times that an edge overloads in the cascading propagation, we discuss how to protect the edges with the different load. Our results are useful not only for improving significantly the robustness of complex networks but also for further studying on the control and defense of cascading failures. Content Type Journal Article Category Original Paper Pages 1-9 DOI 10.1007/s11071-012-0587-8 Authors Jianwei Wang, School of Business Administration, Northeastern University, Shenyang, 110819 P.R. China Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    A substitution box (S-box) plays a central role in cryptographic algorithms. In this paper, an efficient method for designing S-boxes based on chaotic maps is proposed. The proposed method is based on the NCA (nonlinear chaotic algorithm) chaotic maps. The S-box so constructed has very optimal nonlinearity, bit independence criterion (BIC), strict avalanche criterion (SAC), differential and linear approximation probabilities. The proposed S-box is more secure against differential and linear cryptanalysis compared to recently proposed chaotic S-boxes. Content Type Journal Article Category Original Paper Pages 1-4 DOI 10.1007/s11071-012-0573-1 Authors Iqtadar Hussain, Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan Tariq Shah, Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan Muhammad Asif Gondal, Department of Sciences and Humanities, National University of Computer and Emerging Sciences, Islamabad, Pakistan Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    Perturbation methods are routinely used in all fields of applied mathematics where analytical solutions for nonlinear dynamical systems are searched. Among them, normal form theory provides a reliable method for systematically simplifying dynamical systems via nonlinear change of coordinates, and is also used in a mechanical context to define Nonlinear Normal Modes (NNMs). The main recognized drawback of perturbation methods is the absence of a criterion establishing their range of validity in terms of amplitude. In this paper, we propose a method to obtain upper bounds for amplitudes of changes of variables in normal form transformations. The criterion is tested on simple mechanical systems with one and two degrees-of-freedom, and for complex as well as real normal form. Its behavior with increasing order in the normal transform is established, and comparisons are drawn between exact solutions and normal form computations for increasing levels of amplitudes. The results clearly establish that the criterion gives an upper bound for validity limit of normal transforms. Content Type Journal Article Category Original Paper Pages 1-19 DOI 10.1007/s11071-012-0584-y Authors Claude-Henri Lamarque, Université de Lyon, ENTPE/DGCB/FRE CNRS 3237, Rue Maurice Audin, 69518 Vaulx-en-Velin Cedex, France Cyril Touzé, Unité de Mécanique (UME), ENSTA—ParisTech, Paris, France Olivier Thomas, Structural Mechanics and Coupled Systems Laboratory, CNAM, Paris, France Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    This paper describes a prey–predator fishery system with prey dispersal in a two-patch environment, one of which is a free fishing zone and the other a protected zone. The proposed system reflects the dynamic interaction between the net economic revenue and the fishing effort used to harvest the population in presence of a suitable tax. Local as well as global stability of the system is analyzed. The optimal taxation policy is formulated and solved with the help of Pontryagin’s maximal principle. The objective of the paper is to achieve the sustainability of the fishery, keeping the ecological balance, and maximize the monetary social benefit. The dynamical behavior of the delay system is further analyzed through incorporating discrete type gestational delay of predators, and the existence of Hopf bifurcation phenomenon is checked at the interior equilibrium point. Moreover, we use normal form method and center manifold theorem to examine the nature of the Hopf bifurcation. Theoretical results are verified with the help of numerical examples and graphical illustrations. Content Type Journal Article Category Original Paper Pages 1-25 DOI 10.1007/s11071-012-0575-z Authors Kunal Chakraborty, Information Services and Ocean Sciences Group, Indian National Centre for Ocean Information Services, Hyderabad “Ocean Valley”, Pragathi Nagar (BO), Nizampet (SO), Hyderabad, 500090 India Soovoojeet Jana, Department of Mathematics, Bengal Engineering and Science University, Shibpur, Howrah, 711103 India T. K. Kar, Department of Mathematics, Bengal Engineering and Science University, Shibpur, Howrah, 711103 India Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    We investigate the model selection problem for nonlinear autoregressive with exogenous variables models estimated using the weighted least squares (WLS) method. Because WLS changes the statistical property of data under study and violates the assumptions imposed on the well-developed model evaluation and selection methods (e.g. Akaike’s information criterion, Schwarz’s Bayesian information criterion, and the error reduction ratio based methods), therefore, new approaches should be investigated. In this research, an information criterion based method and two l 1 -norm regularization methods are taken into consideration: (a) in the former method, for models estimated using WLS, we first derive an information criterion in terms of the generalized information criterion (GIC, proposed by Konishi and Kitagawa in Biometrica 83(4):875–890, 1996 ), which is a theoretical framework for the analysis and extension of information criteria via a statistical functional approach. Then we develop a robust selection procedure by combining the GIC-based forward stepwise method with Subsampling; (b) in the latter two methods, we employ the l 1 -norm regularization methods, including Lasso and adaptive Lasso, to select models estimated with WLS. Finally, a numerical example is given to test and compare the performance of the three methods. Content Type Journal Article Category Original Paper Pages 1-16 DOI 10.1007/s11071-012-0576-y Authors Pan Qin, Institute of Mathematics for Industry, Kyushu University, 744 Motooka, Fukuoka, Japan Ryuei Nishii, Institute of Mathematics for Industry, Kyushu University, 744 Motooka, Fukuoka, Japan Zi-Jiang Yang, Department of Intelligent Systems Engineering, Ibaraki University, 4-12-1 Nakanarusawa, Ibaraki, Japan Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    In this paper, the moment Lyapunov exponent and stochastic stability of binary airfoil subjected to non-Gaussian colored noise are investigated. The noise is simplified to an Ornstein–Uhlenbeck process by applying a path-integral approach. Via the singular perturbation method, the second-order expansions of the moment Lyapunov exponent are obtained, which agree with the results obtained using the Monte Carlo simulation well. Finally, the effects of the noise and system parameters on the stochastic stability of the binary airfoil system are discussed. Content Type Journal Article Category Original Paper Pages 1-13 DOI 10.1007/s11071-012-0577-x Authors D. L. Hu, State Key Lab of Mechanics and Control for Mechanical Structures, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, 29 YuDao Street, Nanjing, 210016 P.R. China Y. Huang, State Key Lab of Mechanics and Control for Mechanical Structures, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, 29 YuDao Street, Nanjing, 210016 P.R. China X. B. Liu, State Key Lab of Mechanics and Control for Mechanical Structures, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, 29 YuDao Street, Nanjing, 210016 P.R. China Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    The interactions between subsystems are important for large-scale systems, which render the whole system highly nonlinear. In this paper, we address the optimal distributed filtering problem for a kind of local strongly coupled systems. The coupled systems interact by communication in which there are random delays and data dropouts. First, we conduct a strongly coupled system with communication between the nodes. Applying the standard Kalman filter design procedures to such systems is difficult because of transmission delay and intermittent communication. Then, we use the stochastic theory and state augmentation technique for the proposed systems. We present the optimal filtering problem in terms of the full system dynamics. Finally, the numerical simulations show the effectiveness of the filtering method proposed. Content Type Journal Article Category Review Pages 1-8 DOI 10.1007/s11071-012-0588-7 Authors Yunze Cai, Department of Automation, Shanghai Jiao Tong University, Shanghai, 200240 P.R. China Jun Lu, Department of Automation, Shanghai Jiao Tong University, Shanghai, 200240 P.R. China O. Hua Wang, Department of Mechanical Engineering, Boston University, Boston, MA 02215, USA Xiaoming Xu, Department of Automation, Shanghai Jiao Tong University, Shanghai, 200240 P.R. China Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    Two-dimensional parity-time ( PT ) symmetric potentials are introduced, which allow the existence of spatial solitons in the model of the strongly nonlocal nonlinear Schrödinger equation. Two-dimensional accessible solitons are found in the form of solutions separating the radial amplitude, given in terms of Laguerre polynomials, a phase function involving quadratic, linear, and constant phase shifts, and a specific azimuthal modulation function. Shape-preserving solitons are constructed from Laguerre–Gaussian functions containing the self-similar variable and an exponential form of the azimuthal modulation, containing sine and cosine functions, when a suitable PT -symmetric potential is chosen. Interesting soliton profiles and the corresponding PT -symmetric potentials are displayed for different values of the parameters. Content Type Journal Article Category Original Paper Pages 1-8 DOI 10.1007/s11071-012-0594-9 Authors Wei-Ping Zhong, Department of Electronic and Information Engineering, Shunde Polytechnic, Guangdong Province, Shunde 528300, China Milivoj R. Belić, Texas A&M University at Qatar, P.O. Box 23874, Doha, Qatar Tingwen Huang, Texas A&M University at Qatar, P.O. Box 23874, Doha, Qatar Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    In this paper, a precise tracking control method for piezoelectric actuators based on a hysteresis observer is considered. A nonlinear observer to estimate the hysteretic nonlinearity in the piezoelectric actuator is designed, and then the hysteretic nonlinearity is compensated for by a feedforward control. The proposed observer is easy to design and has better performance compared to the previous work presented in the literature. A feedback controller is also designed to track reference signals. A numerical simulation is presented to verify the method proposed. Content Type Journal Article Category Original Paper Pages 1-8 DOI 10.1007/s11071-012-0589-6 Authors D. H. Ji, Mobile communication Division, Digital Media and Communications, Samsung Electronics, Co. Ltd., Maetan-dong, Suwon, Gyeonggi-do, 416-2 Korea J. H. Koo, Research & Development Division, Hyundai Motor Group, Yong-in, Republic of Korea W. J. Yoo, Mobile communication Division, Digital Media and Communications, Samsung Electronics, Co. Ltd., Maetan-dong, Suwon, Gyeonggi-do, 416-2 Korea Ju H. Park, Nonlinear Dynamics Group, Department of Electrical Engineering, Yeungnam University, 214-1 Dae-Dong, Kyongsan, 712-749 Republic of Korea Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    This paper presents an investigation on the nonlinear dynamic response of carbon nanotube-reinforced composite (CNTRC) plates resting on elastic foundations in thermal environments. Two configurations, i.e., single-layer CNTRC plate and three-layer plate that is composed of a homogeneous core layer and two CNTRC surface sheets, are considered. The single-walled carbon nanotube (SWCNT) reinforcement is either uniformly distributed (UD) or functionally graded (FG) in the thickness direction. The material properties of FG-CNTRC plates are assumed to be graded in the thickness direction, and are estimated through a micromechanical model. The motion equations are based on a higher-order shear deformation theory with a von Kármán-type of kinematic nonlinearity. The thermal effects are also included and the material properties of CNTRCs are assumed to be temperature-dependent. The equations of motion that includes plate-foundation interaction are solved by a two-step perturbation technique. Two cases of the in-plane boundary conditions are considered. Initial stresses caused by thermal loads or in-plane edge loads are introduced. The effects of material property gradient, the volume fraction distribution, the foundation stiffness, the temperature change, the initial stress, and the core-to-face sheet thickness ratio on the dynamic response of CNTRC plates are discussed in detail through a parametric study. Content Type Journal Article Category Original Paper Pages 1-20 DOI 10.1007/s11071-012-0491-2 Authors Zhen-Xin Wang, School of Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai, 200030 People’s Republic of China Hui-Shen Shen, School of Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai, 200030 People’s Republic of China Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    A geometrically exact mechanical model for the overall dynamics of elastic isotropic rotating blades is proposed. The mechanical formulation is based on the special Cosserat theory of rods which includes all geometric terms in the kinematics and in the balance laws without any restriction on the geometry of deformation besides the enforcement of the local rigidity of the blade cross sections. All apparent forces acting on the blade moving in a rotating frame are accounted for in exact form. The role of internal kinematic constraints such as the unshearability of the slender blades is discussed. The Taylor expansion of the governing equations obtained via an Updated Lagrangian formulation is then employed to obtain the linearized perturbed form about the prestressed configuration under the centrifugal forces. By applying the Galerkin approach to the linearized equations of motion, the linear eigenvalue problem is solved to yield the frequencies and mode shapes. In particular, the natural frequencies of unshearable blades including coupling between flapping, lagging, axial and torsional components are investigated. The angular speeds at which internal resonances may arise due to specific ratios between the frequencies of different modes are determined thus shedding light onto the overall modal couplings in rotating beam structures depending on the angular speed regime. The companion paper (part 2) discusses the nonlinear modes of vibration away from internal resonances. Content Type Journal Article Category Original Paper Pages 1-17 DOI 10.1007/s11071-012-0486-z Authors Walter Lacarbonara, Dipartimento di Ingegneria Strutturale, Universitá degli Studi di Roma La Sapienza, Via Eudossiana 18, 00184 Rome, Italy Hadi Arvin, Department of Mechanical Engineering, Amirkabir University of Technology, 424 Hafez Ave, Tehran, Iran Firooz Bakhtiari-Nejad, Department of Mechanical Engineering, Amirkabir University of Technology, 424 Hafez Ave, Tehran, Iran Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    We give an overview of a selection of studies on fractional operations of integration and differentiation of variable order, when this order may vary from point to point. We touch on both the Euclidean setting and also the general setting within the framework of quasimetric measure spaces. Content Type Journal Article Category Review Pages 1-10 DOI 10.1007/s11071-012-0485-0 Authors Stefan Samko, University of Algarve, Faro, Portugal Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    This paper presents a new parallel algorithm for dynamics simulation of general multibody systems. The developed formulations are iterative and possess divide and conquer structure. The constraints equations are imposed at the acceleration level. Augmented Lagrangian methods with mass-orthogonal projections are used to prevent from constraint violation errors. The proposed approaches treat tree topology mechanisms or multibody systems which contain kinematic closed loops in a uniform manner and can handle problems with rank deficient Jacobian matrices. Test case results indicate good accuracy performance dependent on the expense put in the iterative correction of constraint equations. Good numerical properties and robustness of the algorithms are observed when handling systems with single and coupled kinematic loops, redundant constraints, which may repeatedly enter singular configurations. Content Type Journal Article Category Original Paper Pages 1-19 DOI 10.1007/s11071-012-0503-2 Authors Paweł Malczyk, Institute of Aeronautics and Applied Mechanics, Faculty of Power and Aeronautical Engineering, Warsaw University of Technology, Nowowiejska 24, 00-665 Warsaw, Poland Janusz Frączek, Institute of Aeronautics and Applied Mechanics, Faculty of Power and Aeronautical Engineering, Warsaw University of Technology, Nowowiejska 24, 00-665 Warsaw, Poland Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    A symbolic computation scheme and its corresponding Maple program are developed to compute the normal form for the Hopf bifurcation in a neutral delay differential equation. In the symbolic computation scheme, the neutral delay differential equation is considered as an ordinary differential equation in an appropriate infinite-dimensional phase space so that both center manifold reduction and normal form computation can be simultaneously conducted without computing center manifold beforehand. The Maple program is proved to provide an easy way to compute the normal form of the neutral delay differential equation automatically by only inputting some basic information of the equation. As an illustrative example, the application of the Maple program to a container crane with a delayed position feedback control is given. The results reveal that the normal form obtained by using the center manifold reduction and the normal form computation is in a full agreement with the result derived by applying the method of multiple scales. Moreover, numerical analysis is presented to validate the analytical results. Content Type Journal Article Category Original Paper Pages 1-11 DOI 10.1007/s11071-012-0468-1 Authors Li Zhang, State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, No. 29 Yudao Street, Nanjing, 210016 China Huailei Wang, State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, No. 29 Yudao Street, Nanjing, 210016 China Haiyan Hu, State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, No. 29 Yudao Street, Nanjing, 210016 China Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    Nonlinear Schrödinger-type equations can model the nonlinear waves in fluids, plasmas, nonlinear optics and atmosphere. In this paper, integrable coupled nonlinear Schrödinger-type equations are investigated. With the aid of symbolic computation, the equations are transformed into their bilinear forms, by virtue of which the multi-soliton solutions are derived. Soliton interactions are analyzed, the elastic interactions are seen, while the dark, anti-dark, M- and W-shape solitons are exhibited with some parameters selected. The propagating solitons can preserve their properties after the interaction, and the profiles of them depend on the corresponding dispersion relations. The amplitudes, velocities of the solitons are found to be influenced by the coefficient of the original equations, which is detailed in the paper. Content Type Journal Article Category Original Paper Pages 1-9 DOI 10.1007/s11071-012-0481-4 Authors Gao-Qing Meng, Ministry-of-Education Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics, Beijing, 100191 China Yi-Tian Gao, Ministry-of-Education Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics, Beijing, 100191 China Xin Yu, Ministry-of-Education Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics, Beijing, 100191 China Yu-Jia Shen, Ministry-of-Education Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics, Beijing, 100191 China Yi Qin, Ministry-of-Education Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics, Beijing, 100191 China Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X

Beschreibung:    The electro-mechanical gyrostat system has become a fundamental model of nonlinear dynamics due to its potential applications in practical engineering. It has also been intensively investigated in the last few years due to its intrinsic and complex nonlinear dynamical behaviors. This paper is mainly concerned on the issues of impulsive stabilization and synchronization of chaotic electro-mechanical gyrostat systems. Based on the practical stability theory of impulsive dynamical systems, some simple yet less conservative criteria ensuring impulsive stabilization and synchronization of electro-mechanical gyrostat systems are derived. Subsequently, numerical simulations are presented to demonstrate the effectiveness of the proposed control techniques. Content Type Journal Article Category Original Paper Pages 1-9 DOI 10.1007/s11071-012-0474-3 Authors Lifang Cai, Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai, 200072 China Jin Zhou, Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai, 200072 China Journal Nonlinear Dynamics Online ISSN 1573-269X Print ISSN 0924-090X