ALBERT

Description:    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

Description: 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

Description:    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

Description:    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

Description:    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

Description:    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

Description:    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

Description:    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

Description:    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

Description:    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