ALBERT

Description: Adaptive infinite impulse response filters have received much attention due to its utilization in a wide range of real-world applications. The design of the IIR filters poses a typically nonlinear, non-differentiable and multimodal problem in the estimation of the coefficient parameters. The aim of the current study is the application of a novel hybrid optimization technique based on the combination of cellular particle swarm optimization and differential evolution called CPSO–DE for the optimal parameter estimation of IIR filters. DE is used as the evolution rule of the cellular part in CPSO to improve the performance of the original CPSO. Benchmark IIR systems commonly used in the specialized literature have been selected for tuning the parameters and demonstrating the effectiveness of the CPSO–DE method. The proposed CPSO–DE method is experimentally compared with two new design methods: the tissue-like membrane system (TMS), the hybrid particle swarm optimization and gravitational search algorithm (HPSO–GSA), the original CPSO-outer and CPSO-inner, and classical implementations of PSO, GSA and DE. Computational results and comparison of CPSO–DE with the other evolutionary and hybrid methods show satisfactory results. The hybridization of CPSO and DE demonstrates powerful estimation ability. In particular, to our knowledge, this hybridization has not yet been investigated for the IIR system identification.

Description: The responses of electrically coupled neuronal network to external stimulus injected on a single neuron are investigated. Stimulating the largest-degree neuron in the network, it is found that as the intensity of the stimulus increases, the network will be transiting from the resting to firing states and then restoring to the resting state, thereby showing a bounded firing region in the parameter space. Furthermore, it is found that as the coupling strength among the neurons decreases, the firing region is gradually expanded and, at the weak couplings, it could be separated into several disconnected subregions. By a simplified network model, we conduct a detailed analysis on the bifurcation diagram of the network dynamics in the two-dimensional parameter space spanned by stimulating intensity and coupling strength, and, by introducing a new coefficient named effective stimulus, explore the underlying mechanisms for the modified firing region. It is revealed that the coupling strength and stimulating intensity are equally important in evoking the network, but with different mechanisms. Specifically, the effective stimuli are shifted up globally by increasing the stimulating intensity, while are drawn closer by increasing the coupling strength. The dynamical responses of small-world and random complex networks to external stimulus are also investigated, which confirm the generality of the observed phenomena. The findings shed new lights on the collective behaviors of complex neuronal networks and might help our understandings on the recent experimental results.

Description: In this paper, we propose a novel meminductor model for exploring its characteristics. By using this model, a simple meminductor-based circuit with three elements is constructed. Stability and dynamical behaviors of the circuit are investigated in detail. The study finds that the system has complicated nonlinear phenomena, such as coexisting bifurcation modes, coexisting attractors, and two different kinds of chaotic transients. Furthermore, by the circuit experiment, the chaotic characteristics of the system are confirmed, which illustrates the validity of the theoretical analysis.

Description: Equalization filtering is an effective technique applied to minimize the inter-symbol interference (ISI) in multipath fading channels; the problem gets worse for higher-order constellations which are required for high data rates in today’s communication systems. The least mean square (LMS) filter is a computationally efficient and easily implementable algorithm but suffers from slow convergence; highly complex filters are required to nullify the effects of ISI. In this paper, we develop complex modified fractional-order (FO) nonlinear variants of the LMS and the NLMS algorithms and apply in adaptive channel equalization, in both feed-forward and decision feedback configurations. In addition to the standard first-order derivative, the update in the modified LMS also depends on the FO derivative of the mean square error, the final update is formed using a combination of conventional update term and a nonlinear term obtained through Riemann–Liouville fractional derivative. The step size of the FNLMS scheme in fractional part is not only a function of the input energy but also the FO. The differintegral operator working as differentiator helps improve the convergence rate because the algorithm becomes nonlinear; the fractional algorithms provide more parameters to control the rate of convergence and have simple implementation with almost similar complexity. The performances of the schemes are validated through extensive simulation results for block fading channels (frequency flat and selective) to evaluate the symbol error rate for higher-order quadrature amplitude modulation schemes, mean square error and combined channel and equalizer responses to show the improved inverse modeling of the channel. Simulation experiments confirm the superiority of the proposed algorithm over the traditional counterparts.

Description: This paper studies the exponential cluster synchronization problem of complex dynamical networks with delayed couplings and nonidentical nodes. A new type of pinning impulsive control approach is proposed to achieve the exponential cluster synchronization of the considered network. By employing a time-dependent Lyapunov functional, less conservative cluster synchronization criteria are established in the form of linear matrix inequalities. Compared with the existing works, the constructed Lyapunov functional is related with impulse time sequence, which makes full use of the information on dynamical characteristic of synchronization error dynamics. Finally, a numerical example of typical chua’s system is given to illustrate the effectiveness and correctness of the theoretical results.

Description: The effect of vibrational smoothing of dry friction has been studied intensively in the past. High-frequency vibrations have been shown to reduce average friction forces and thus smooth the effective characteristics of dry friction. Consequently, undesired friction-induced phenomena, such as friction-induced vibrations or stick-slip motion, can be avoided. While most publications focus on rigid contacts using classical Coulomb friction models, a class of dynamic friction models, namely the Dahl, LuGre and the elasto-plastic model proposed by Dupont et al., is considered here in order to account for contact compliance. Based on a simple 1-DoF friction oscillator, the effect of longitudinal high-frequency vibrations is investigated. An averaging procedure is applied in order to derive the effective friction–velocity characteristics of the system. Using a Galerkin procedure, analytical approximations can be derived for the Dahl and the LuGre friction model, while numerical calculations have to be performed for the elasto-plastic model. In order to validate the results, full timescale numerical simulations are performed. When accounting for contact compliance, the smoothing effect can still be observed. However, the calculated friction forces are higher compared to the classical results using Coulomb friction. Hence, the assumption of a rigid contact leads to overestimation of the smoothing effect.

Description: A new procedure for designing optimal bounded control of stochastically excited multi-degree-of-freedom (MDOF) nonlinear viscoelastic systems is proposed based on the stochastic averaging method and the stochastic maximum principle. First, the system is formulated as a quasi-integrable Hamiltonian system with viscoelastic terms and each viscoelastic term is replaced approximately by an elastically restoring force and a visco-damping force based on the randomly periodic behavior of the motion of quasi-integrable Hamiltonian system. Thus, a stochastically excited MDOF nonlinear viscoelastic system is converted to an equivalent quasi-integrable Hamiltonian system without viscoelastic terms. Then, by applying stochastic averaging, the system is further reduced to a partially averaged system of less dimension. The adjoint equation and maximum condition for the optimal control problem of the partially averaged system are derived by using the stochastic maximum principle, and the optimal bounded control force is determined from the maximum condition. Finally, the probability and statistics of the stationary response of optimally controlled system are obtained by solving the Fokker–Plank–Kolmogorov equation (FPK) associated with the fully averaged Itô equation of the controlled system. An example is worked out to illustrate the proposed procedure and its effectiveness.

Description: In this paper, synchronization of master–slave Lagrangian systems via intermittent control was developed. Based on the intermittent control, some algebraic criteria are derived to make the slave Lagrangian system synchronize to a master one. Different from the most existing results on control problems of Lagrangian systems, the controller proposed here is not continuous-time control input and is not relied on the knowledge of system models. As a direct application, the obtained results are applied to a typical two-link revolute jointed robot (robot manipulator). Subsequently, numerical simulations demonstrate the effectiveness of the criteria and the robustness of the control strategy.

Description: The paper designs new 2- and 3-stage Radau IIA algorithms to integrate the dynamic responses of flexible multibody system with holonomic constraints. The total translation, the incremental rotation and associated velocities are selected as unknowns to avoid the linearization of angular acceleration which makes it possible to parameterize the finite rotation by using the Wiener–Milenković parameters. The new algorithms release the heavy computational burden through the simplified Newton iterations and are stabilized by the preferable h -scaling technique. Contributions of the paper include: (1) For 2-stage algorithm, the resulting block triangular equations are solved efficiently by an inner iteration scheme. (2) For 3-stage algorithm, the full-size linear system is decoupled into a real and a complex subsystems which reduces the size of the system dramatically. (3) A new scheme is designed to predict the truncation error from the associated deferred correction equations without overestimation. Finally, numerical simulations show the 2- and 3-stage Radau IIA algorithms have excellent stability and convergence properties and behavior in a computationally efficient manner.

Description: We investigate the systematic generation of higher-order solitons and breathers of the Hirota equation on different backgrounds. The Darboux transformation is used to construct proper initial conditions for dynamical generation of high-intensity solitons and breathers of different orders on a uniform background. We provide expressions for the Lax pair generating functions and the procedure for calculating higher-order solutions when Jacobi elliptic functions are the background seed solutions of the Hirota equation. We confirm that the peak height of each soliton or breather in the nonlinear Darboux superposition adds linearly, to form the intensity maximum of the final solution.

Description: In this paper we propose a novel technique to decompose networked systems and use this technique to investigate the dynamics of connected vehicle networks with wireless vehicle-to-vehicle (V2V) communication. We apply modal perturbation analysis to approximate the modes of the perturbed network about the modes of the corresponding cyclically symmetric network. By exploiting the cyclic symmetry, we approximate the dynamics of a given mode by solving a small number of linear algebraic equations. We apply this approach to decompose connected vehicle networks into traveling waves which allows us to assess the impacts of long-range V2V communication on the stability of traffic flow.

Description: This article aims to study the three-dimensional motion of a rigid body that rotates about one of its fixed points. The effects of both a Newtonian force field and a moment of a gyrostat are taken into account. In the present work, we have assumed that the body has a spindle initial speed about one of the principal axes of the ellipsoid of inertia. The approximate solutions of the nonlinear problem are obtained by utilizing the Krylov–Bogoliubov–Mitropolski (KBM) technique and its amendments. Such solutions are demonstrated and then illustrated graphically in order to provide an extensive description of the body motion at any time. It is justified that the attained results are in a well consistency with those of the previous works, which are considered as limiting cases. The numerical solutions for governing system of motion are achieved using the fourth-order Runge–Kutta method and represented graphically. The comparison between the analytical solutions and the numerical ones reveals high consistency between them.

Description: For underactuated overhead cranes with payload hoisting/lowering, a partially saturated adaptive controller subject to unknown or uncertain system parameters is presented in this paper. To decrease the convergence time in the case of the overhead crane parameters already experienced by the system, the learning component is added to the proposed partially saturated adaptive controller. By introducing hyperbolic tangent functions into the control methods, the proposed controllers can guarantee soft trolley start even in the case of high initial velocities of trolley and cable. The convergence and stability performance of the closed-loop system is proven by Lyapunov techniques and LaSalle’s invariance theorem. Simulation results are listed to verify the adaptive performance with reduced actuating forces and strong robustness with respect to different external disturbances of the proposed controllers.

Description: Due to resource constraints in wireless sensor networks and the presence of unwanted conditions in communication systems and transmission channels, the suggestion of a robust method which provides battery lifetime increment and relative security is of vital importance. This paper considers the secure communication in wireless sensor networks based on new robust adaptive finite time chaos synchronization approach in the presence of noise and uncertainty. For this purpose, the modified Chua oscillators are added to the base station and sensor nodes to generate the chaotic signals. Chaotic signals are impregnated with the noise and uncertainty. At first, we apply the modified independent component analysis to separate the noise from the chaotic signals. Then, using the adaptive finite-time sliding mode controller, a control law and an adaptive parameter-tuning method is proposed to achieve the finite-time chaos synchronization under the noisy conditions and parametric uncertainties. Synchronization between the base station and each of the sensor nodes is realized by multiplying a selection matrix by the specified chaotic signal which is broadcasted by the base station to the sensor nodes. Simulation results are presented to show the effectiveness and applicability of the proposed technique.

Description: The global bifurcations and multi-pulse orbits of an aero-thermo-elastic functionally graded material (FGM) truncated conical shell under complex loads are investigated with the case of 1:2 internal resonance and primary parametric resonance. The method of multiple scales is utilized to obtain the averaged equations. Based on the averaged equations obtained, the normal form theory is employed to find the explicit expressions of normal form associated with a double zero and a pair of pure imaginary eigenvalues. The energy-phase method developed by Haller and Wiggins is used to analyze the multi-pulse homoclinic bifurcations and chaotic dynamics of the FGM truncated conical shell. The analytical results obtained here indicate that there exist the multi-pulse Shilnikov-type homoclinic orbits for the resonant case which may result in chaos in the system. Homoclinic trees which describe the repeated bifurcations of multi-pulse solutions are found. The diagrams show a gradual breakup of the homoclinic tree in the system as the dissipation factor is increased. Numerical simulations are presented to illustrate that for the FGM truncated conical shell, the multi-pulse Shilnikov-type chaotic motions can occur. The influence of the structural-damping, the aerodynamic-damping, and the in-plane and transverse excitations on the system dynamic behaviors is also discussed by numerical simulations. The results obtained here mean the existence of chaos in the sense of the Smale horseshoes for the FGM truncated conical shell.

Description: The paper reports the simplest 4-D dissipative autonomous chaotic system with line of equilibria and many unique properties. The dynamics of the new system contains a total of eight terms with one nonlinear term. It has one bifurcation parameter. Therefore, the proposed chaotic system is the simplest compared with the other similar 4-D systems. The Jacobian matrix of the new system has rank less than four. However, the proposed system exhibits four distinct Lyapunov exponents with \((+, 0, -, -)\) sign for some values of parameter and thus confirms the presence of chaos. Further, the system shows chaotic 2-torus \((+,0,0,-)\) , quasi-periodic \([(0,0,-,-), (0,0,0,-)]\) and multistability behaviour. Bifurcation diagram, Lyapunov spectrum, phase portrait, instantaneous phase plot, Poincaré map, frequency spectrum, recurrence analysis, 0–1 test, sensitivity to initial conditions and circuit simulation are used to analyse and describe the complex and rich dynamic behaviour of the proposed system. The hardware circuit realisation of the new system validates the MATLAB simulation results. The new system is developed from the well-known Rossler type-IV 3-D chaotic system.

Description: In this paper, a novel multidimensional scaling (MDS) based on information measures method is proposed to analyze financial stock markets. In order to examine the effectiveness of this method, we applied it to the classification of two types of artificial series, the logistic map model and the cubic map model, as well as stock time series. Moreover, the traditional MDS using Euclidean dissimilarity is also provided as a reference for comparisons. The results show that the MDS based on information measures can give us more detailed, exact and clearer information on the classification of simulation series and stock time series than the MDS using Euclidean dissimilarity. In addition, the proposed graphical method may also assist in the construction of multivariate econometric models.

Description: In this paper, a model predictive control (MPC) scheme based on Hammerstein model is carried on. The use of such nonlinear models complicates the implementation of the MPC in terms of computational time and burden since a nonlinear and so a nonconvex optimization problem will result. The Nelder Mead (NM) algorithm, as a free derivative method, is used to solve the resulting optimization problem. NM algorithm proves its efficiency in terms of computation time and global optimum seeking that can be successfully exploited especially with fast dynamic systems. A comparative study between the NM algorithm and the gradient-based method (GBM) based on computation time is established. The efficiency of the NM algorithm is illustrated with SISO and MIMO examples compared to GBM algorithm.

Description: Novel chaotic system designs and their engineering applications have received considerable critical attention. In this paper, a new three-dimensional chaotic system and its application are introduced. The interesting aspects of this chaotic system are the absence of equilibrium points and the coexisting of limit cycle and torus. Basic dynamics of the no-equilibrium system have been executed by means of phase portraits, bifurcation diagram, continuation, and Lyapunov exponents. Experimental results of the electronic circuit realizing the no-equilibrium system have been reported to show system’s feasibility. By using the chaoticity of the new system without equilibrium, we have developed a random bit generator for practical signal encryption application. Numerical results illustrate the usefulness of the random bit generator.

Description: In this paper, a linear and adaptive feedback pinning strategy is used to study the lag synchronization of complex dynamical networks with known state time-delay and unknown channel time-delay. Firstly, based on the Lyapunov stability theory, a novel Lyapunov functional, which involves the estimated error \(\hat{e}_{i}(t)\) rather than the general synchronization error \(e_{i}(t)\) , is constructed. Secondly, in view of the unknown information of the channel time-delay, two available pinning controllers are designed such that the considered networks achieve lag synchronization. Furthermore, by a proper adaptation mechanism, we estimate the unknown channel time-delay successfully under the case that the initial value of the estimated channel time-delay is larger than true channel time-delay, i.e., \(\hat{\tau }(0)〉\tau \) and the another case \(\hat{\tau }(0)〈\tau \) . Finally, the effectiveness and correctness of the lag synchronization criteria are verified through two simulation experiments.

Description: Neuron can receive electric signals or forcing currents from more than one channel, and these forcing currents could show some diversity. Based on the Hindmarsh–Rose neuron model, mixed forcing currents, which are composed of low-frequency, high-frequency and constant signals, are imposed on the neuron, and multiple modes of electric activities could be observed alternately (in turn) from the neuron. Based on the Helmholtz theorem, the Hamilton energy is calculated to discern the energy dependence on the mode selection of the electric activities of neuron. It is found that the response of electrical activities much depends on the amplitude than the frequency when mixed signals are imposed on the neuron synchronously; however, the rhythm of electrical activities could be adjusted by the frequency of the periodical signals in the mixed signal. It is confirmed that the energy is much dependent on the mode of electrical activities instead of the external forcing currents directly, and a smaller energy occurs under bursting states. The delayed response of Hamilton energy to external forcing currents confirms that neuron contributes to energy coding. These results could be helpful for further investigation on energy problems in neuronal network associated with model transition for collective behaviors.

Description: In this paper, we investigate outer synchronization of two small-world dynamical networks via second-order sliding mode control strategy. In particular, based on the coupling feature of the nodes, a message feedback chain is established. And then, the synchronization will be analyzed via pinning some nodes. By means of the second-order sliding mode theory, we propose the effective controller to realize outer synchronization between two small-world networks with a lower cost. Finally, we present some simulations to illustrate the theoretical results.

Description: In this paper, a unified scheme is proposed for solving the classical shortest path problem and the generalized shortest path problem, which are highly nonlinear. Particularly, the generalized shortest path problem is more complex than the classical shortest path problem since it requires finding a shortest path among the paths from a vertex to all the feasible destination vertices. Different from existing results, inspired by the optimality principle of Bellman’s dynamic programming, we formulate the two types of shortest path problems as linear programs with the decision variables denoting the lengths of possible paths. Then, biased consensus neural networks are adopted to solve the corresponding linear programs in an efficient and distributed manner. Theoretical analysis guarantees the performance of the proposed scheme. In addition, two illustrative examples are presented to validate the efficacy of the proposed scheme and the theoretical results. Moreover, an application to mobile robot navigation in a maze further substantiates the efficacy of the proposed scheme.

Description: Fractional partial differential equations have many applications in science and engineering. However, not only the analytical solution existed for a limited number of cases, but also the numerical methods are very complicated and difficult. The aim of this paper is to present an efficient wavelet operational method based on the second Chebyshev wavelet to solve the fractional partial differential equations. We derived the convergence of the two-dimensional second Chebyshev wavelet and give the second Chebyshev wavelet operational matrix of fractional integration. Then we present a computational method based on the above results for solving a class of fractional partial differential equations. The initial equations are transformed into a Sylvester equation. Some numerical examples are given to demonstrate the simplicity, clarity and powerfulness of the new method.

Description: In this paper, we investigate a ratio-dependent prey–predator model with state-dependent impulsive harvesting where the prey growth rate is subject to a strong Allee effect. The existence of order-1 homoclinic cycle is obtained, and choosing \(\alpha \) as a control parameter, the existence, uniqueness and stability of order-1 periodic solution of the system are discussed by means of the geometry theory of semi-continuous dynamic system. We also investigate that system exhibits the phenomenon of homoclinic bifurcation about parameter \(\alpha \) . Moreover, the numerical simulations are provided to show the main results. The used methods are intuitive to prove the existence of order-1 periodic solution and homoclinic bifurcation.

Description: This paper considers a class of nonlinear impulsive Caputo differential equations of fractional order, which models chaotic systems. Computer-assisted proof of chaos suppression by stabilizing the unstable system equilibria is provided. A nonexistence result of periodic solutions is presented, and the commensurate fractional-order Lorenz system is simulated for illustration.

Description: This paper is concerned with the variable-coefficient nonlinear evolution equations, which include the cylindrical KdV types of equations. By the combination of Painlevé analysis and Lie group classification method, the integrable conditions, Bäcklund transformations and Lax pairs of the equations are obtained, all of the geometric vector fields of the equations are presented. Then, the relationship among Lie group classification, Painlevé analysis and CK transformation method is considered. Furthermore, the exact solutions generated from the Bäcklund transformations and symmetry reductions of the vc-KdV types of equations are investigated.

Description: The biological Hodgkin–Huxley model and its simplified versions have confirmed its effectiveness for recognizing and understanding the electrical activities in neurons, and bifurcation analysis is often used to detect the mode transition in neuronal activities. Within the collective behaviors of neurons, neuronal network with different topology is designed to study the synchronization behavior and spatial pattern formation. In this review, the authors give careful comments for the presented neuron models and present some open problems in this field, nonlinear analysis could be effective to further discuss these problems and some results could be helpful to give possible guidance in the field of neurodynamics.

Description: This paper presents fractional order fixed-time nonsingular terminal sliding mode control for stabilization and synchronization of fractional order chaotic systems with uncertainties and disturbances. First, a novel fractional order terminal sliding mode surface is proposed to guarantee the fixed-time convergence of system states along the sliding surface. Second, a nonsingular terminal sliding mode controller is designed to force the system states to reach the sliding surface within fixed-time and remain on it forever. Furthermore, the fractional Lyapunov stability theory is used to prove the fixed-time stability and the robustness of the proposed control scheme and estimate the upper bound of convergence time. Next, the proposed control scheme is applied to the synchronization of two nonidentical fractional order Liu chaotic systems and chaos suppression of fractional order power system. Simulation results verify the effectiveness of the proposed control scheme. Finally, some application issues about the proposed scheme are discussed.

Description: The main failure mode of cylindrical roller bearings (CROBs) is localized surface defects (LSDs) such as spalls and pits on the surface of its races or rollers. However, it is difficult to describe the time-varying deflection excitation (TVDE) generated by a LSD and time-varying contact stiffness excitation due to the changes in contact conditions between the roller and defect by using the previous defect models. In this paper, a new dynamic analysis method is proposed to formulate a LSD more accurately for a CROB dynamic modeling. A two-degree of freedom dynamic model for a CROB with a LSD on its races is proposed, which considers both the TVDE and time-varying contact stiffness coefficient produced by the defect. The load-deflection relationship between the roller and race is considered as non-Hertzian one, which can be used to determine the load-deflection relationship between the logarithmic-profile roller and races of the CROB. The numerical results are compared with the available results from the previous defect models in the literature. Effects of the radial load, defect sizes and types on the contact deformation and contact force between the roller and race are investigated, as well as the vibrations characteristics of the CROB. The results show that the proposed method can describe more accurately a real excitation produced by a LSD located at anywhere in the contact zone between the roller and race, which cannot be captured by the previous model in the literature.

Description: In this paper, a novel video chaotic secure communication scheme and its ARM-embedded hardware implementation are investigated, based on the H.264 selective encryption and multi-core multi-process. A six-dimensional discrete-time hyperchaotic system equipped with a nonlinear nominal matrix is firstly constructed, and the corresponding chaotic encryption algorithm is then designed. During H.264 encoding, the difference components of motion vectors in both the horizontal and vertical directions, as well as the DC transform coefficients, are selectively encrypted by using such a chaotic encryption algorithm, respectively, so as to enhance the safety performance. To improve the processing speed and transmission frame rate of the whole hardware system, an ARM-based hardware platform with multi-core multi-process is further adopted to realize the H.264 selective video chaotic secure communication, where the sender collects and encrypts the original video with four-core four-process mode, and the receiver decrypts the encrypted video with three-core three-process mode, in which one core binds one process. Finally, the security performance of the designed system is tested using the TESTU01 statistical test suites and some other statistical security analysis. Both theoretical analysis and experimental results validate the feasibility and reliability of the proposed scheme.

Description: Rotor system is an important part in rotating machineries. As a matter of fact, rotors are subject to uncertainties inevitably due to occasions such as assembling errors, material properties dispersion and variable working conditions. In order to obtain more reasonable evaluations of dynamic response of rotor systems, uncertainties are recommended to be taken into consideration. In this paper, the dynamic responses of an elastically supported uncertain overhung rotor are studied in which uncertain parameters are treated as unknown-but-bounded interval variables. The finite element method is used to derive the deterministic analysis model. A non-intrusive interval method based on Chebyshev polynomial approximation is proposed to evaluate the uncertain dynamic response of the rotor system. Comparative study of the interval method, the scanning method and the Monte Carlo simulation is carried out to illustrate the effectiveness and accuracy. Deflection upper bounds and lower bounds of the disc are obtained with respect to rotating speed in several typical uncertain cases. Results show that the uncertainties have significant effects on the dynamic behaviours of the rotor system and multiple source small uncertainties can lead to large fluctuations in the dynamic responses.

Description: Static and dynamic analyses of an electrostatic microbeam under repulsive force actuation are presented. The repulsive force, created through a specific electrode configuration, generates a net electrostatic force on the beam pushing it away from the substrate. This allows large out-of-plane actuation and eliminates the pull-in instability. For example, a dynamic amplitude of 15  \(\upmu \) m was recorded for a 500- \(\upmu \) m-long cantilever at a DC voltage of 195 V and an AC voltage of 1 V, while the initial gap was only 2  \(\upmu \) m. This study includes mathematical modeling and simulations for a cantilever and a clamped–clamped beam, as well as experimental validation. The beam is modeled using Euler–Bernoulli beam theory and electromechanical coupling effects. Cantilever tip displacement, clamped–clamped midpoint deflection, and natural frequency shifts are reported. Governing equations are solved numerically using the shooting method, which provides a complete picture of the beam dynamics. The numerical results are verified with experimental data from fabricated beams using PolyMUMPs standard fabrication. Frequency response results reveal a mixed softening and hardening behavior and secondary resonances originating from quadratic and cubic nonlinearities in the governing equations. The analysis provides insight for applications in optical and gas sensors where a large signal-to-noise ratio and, sometimes, a wide frequency bandwidth are desired.

Description: By using various techniques, we investigate the (2 \(+\) 1)-dimensional modified KdV-Calogero–Bogoyavlenskii–Schiff equation. This equation is integrable under the mean of the consistent Riccati expansion method. The truncated Painlevé expansion, the simplified Hirota’s method and other methods are used as powerful vehicles to conduct the analysis. We formally derive, in explicit forms, abundant solutions of distinct physical structures, including multiple soliton solutions, multiple complex soliton solutions, kink solutions and singular solutions.

Description: Based on the Hirota bilinear form of the KP equation, five classes of interaction solutions between lumps and line solitons are generated via Maple symbolic computations. Analyticity is automatically guaranteed for the first four classes of interaction solutions and the last fifth class of interaction solutions with the plus sign and can be easily achieved for the last fifth class of interaction solutions with the minus sign by taking special choices of the involved parameters. The presented interaction solutions reduce to the existing lumps while the hyperbolic function disappears.

Description: In this paper, an approach based on the synergistic use of proper orthogonal decomposition and Kalman filtering is proposed for the online health monitoring of damaged structures. The reduced-order model of a structure is obtained during an (offline) initial training stage of monitoring; afterward, effective estimations of a possible structural damage are provided online by tracking the evolution in time of stiffness parameters and projection bases handled in the model order reduction procedure. Such tracking is accomplished via two Kalman filters: a first (extended) one to deal with the time evolution of a joint state vector, gathering the reduced-order state and the stiffness terms degraded by damage; a second one to deal with the update of the reduced-order model in case of damage evolution. Both filters exploit the information conveyed by measurements of the structural response to the external excitations. Results are reported for a (pseudo-experimental) benchmark test on an eight-story shear building. Capability and performance of the proposed approach are assessed in terms of tracked variation of the stiffness terms of the reduced-order model, identified damage location and speed-up of the whole health monitoring procedure.

Description: Although different hyperjerk systems have been discovered, a few hyperjerk systems can exhibit hyperchaotic behavior. In this work, we introduce a new hyperjerk system with hyperchaotic attractors. By investigating dynamics of the system, we have observed the different coexisting attractors such as coexistence of period-2 attractors, or coexistence of period-2 attractor and quasiperiodic attractor. It is worth noting that this striking phenomenon is rarely reported in a hyperjerk system. The proposed system has been realized with electronic components. The agreement between the simulation and experimental results indicates the feasibility of the hyperjerk system. Moreover, chaos control and synchronization of such hyperjerk system have been also reported.

Description: A low-complexity design problem of tracking scheme for uncertain nonholonomic mobile robots is investigated in the presence of unknown time-varying input delay. It is assumed that nonlinearities and parameters of robots and their bounds are unknown. Based on a nonlinear error transformation, a tracking control scheme ensuring preassigned bounds of overshoot, convergence rate, and steady-state values of a tracking error is firstly presented in the absence of input delay, without using any adaptive and function approximation mechanism to estimate unknown nonlinearities and model parameters and computing repeated time derivatives of certain signals. Then, we develop a low-complexity tracking scheme to deal with unknown time-varying input delay of mobile robots where some auxiliary signals and design conditions are derived for the design and stability analysis of the proposed tracking scheme. The boundedness of all signals in the closed-loop system and the guarantee of tracking performance with preassigned bounds are established through Lyapunov stability analysis. The validity of the proposed theoretical result is shown by a simulation example.

Description: In this paper, we investigate the local and global bifurcation behaviors of an archetypal self-excited smooth and discontinuous oscillator driven by moving belt friction. The belt friction is described in the sense of Stribeck characteristic to formulate the mathematical model of the proposed system. For such a friction characteristic, the complicated bifurcation behaviors of the system are discussed. The bifurcation of the multiple sliding segments for this self-excited system is exhibited by analytically exploring the collision of tangent points. The Hopf bifurcation of this self-excited system with viscous damping is analyzed by making the examination of the eigenvalues at the steady state and discussing the stability of the limit cycles. The bifurcation diagrams and the corresponding phase portraits are depicted to demonstrate the complicated dynamical behaviors of double tangency bifurcation, the bifurcation of sliding homoclinic orbit to a saddle, subcritical Hopf bifurcation and grazing bifurcation for this system.

Description: This paper proposes a novel adaptive robust controller for the position and attitude tracking of quadrotor unmanned aerial vehicles subjected to additive disturbances and parameter uncertainties. The nonlinear dynamic equations of the quadrotor are obtained by using the Newton–Euler formalism. An emendatory tracking error is introduced to the modified controller to prevent the system and adaption law from degradation or even instability due to control input saturation caused by actuator constraints. The stability of the closed-loop aircraft system under the proposed control law is guaranteed via Lyapunov theory despite the sustained disturbances and actuator saturation. Simulation results are presented to demonstrate the effectiveness of the proposed control method, and the robustness against unknown nonlinear dynamics caused by parametric uncertainties.

Description: In this paper, a new lattice hydrodynamic model (LH model) of traffic flow under consideration of reaction time of drivers and a corresponding feedback control scheme are proposed. Based on the model, stability analysis is conducted through linear stability analysis of transfer function. The obtained phase diagram indicates that the reaction time of driver can affect the instability region of traffic flow. Under the action of a feedback control, the unstable region is shrunken to reach suppressing jams. The numerical simulations are performed to validate the effect of reaction time of driver in the new LH model. The study results confirm that the reaction time of driver significantly affects the unstability of traffic system, and the feedback control can suppress traffic jams. Furthermore, it is found that the traffic system from the chaotic traffic state to periodic steady one is successfully realizing the control of traffic system.

Description: By using the standard symmetry reduction method, some exact analytical solutions including gray solitons and gray soliton lattice solutions are derived for the ( \(2+1\) )-dimensional nonlinear optical media with periodic nonlocal response. Furthermore, dark/gray soliton solutions and dark soliton lattice solutions are found by means of hyperbolic function expansion method and elliptic function expansion method for the nonlocal nonlinear system, respectively. It is found that two critical points exist for soliton solutions, and the switching dynamics of solitons may be described by the critical points.

Description: Compound hyper-chaotic system is a chaotic system that combines two or more hyper-chaotic systems. In this paper, we propose a 2-dimensional compound homogeneous hyper-chaotic system (CHHCS) and local binary pattern (LBP)-based image encryption algorithm, which includes the CHHCS-based permutation operation and the LBP-based diffusion operation. Firstly, we employ a new CHHCS and prove the good hyper-chaotic behaviors, and we use CHHCS to permutate the plain image twice to obtain good permutation effect. Then, every permutated pixel is diffused with dynamic LBP operation, which means even the same permutated pixel will be encrypted to different cipher value. Finally, we provide some theoretical analyses and simulations to confirm the security and the validity of the proposed algorithm.

Description: Hysteretic behavior due to some nonlinear sources is a common phenomenon in many dynamical systems. One of the sources of this behavior in mechanical systems is dry friction. Dry friction in bolted or riveted joints of mechanical structures makes their dynamic behavior hysteretic. Bi-linear hysteresis is one of the models that can be used to study these systems which is used in this paper. A SDOF system containing a bi-linear hysteretic element called Jenkins element under harmonic, impulse and random excitations is considered. For all three types of excitations, the effects of system and excitation parameters on the defined equivalent system parameters and the response specifications are studied. Harmonic balance method is employed for harmonic excitation studies, and optimum friction threshold for minimizing response amplitude is obtained versus other system parameters and response amplitude. Energy balance method is used for impulse excitation through which the desired decaying ratio can be achieved by tuning the friction threshold, depending on stiffness ratio. System under random excitation is investigated by equivalent linearization technique in two steps. At the first step, equivalent properties are obtained versus instantaneous amplitude of response. In this step, the paper contains the parametric study of system in which the variations of equivalent parameters are described when physical parameters of system or input intensity vary. Overall variance of system response is determined in the second step, and optimum sliding threshold is obtained to have minimum overall variance of system response.

Description: We apply the rescaled range analysis (R/S) method to analyze the geospatial scaling behavior and its relevant features, including spatial heterogeneity, a spatially short-range correlation, spatial scale effects and spatial nonstationarity. Our goal is to provide a tentative finding about a theoretical framework construction of geospatial multifractality of attribution-variable-value distribution. To investigate the spatial scaling behavior, the conventional R/S method is extended to a two-dimensionally geographical space and a two-dimensional geospatially rescaled range analysis method is presented. Our analysis shows that this proposed method is reliable and effective in the analysis of spatial scaling behavior and its characteristics. Furthermore, on the basis of this approach, the theoretical framework of spatial multifractality associated with spatial distribution of attribution value is preliminarily developed. Our findings contribute by providing a potential method to investigate spatial scaling behavior and spatial multifractality.

Description: A systematic investigation of finding Lie point symmetries of certain fractional linear and nonlinear ordinary differential equations is presented. More precisely, Lie point symmetries of fractional Riccati equation, nonhomogeneous fractional linear ordinary differential equation with variable coefficients and quadratic fractional Liénard-type equation in the sense of Riemann–Liouville fractional derivative are derived. Using the obtained Lie point symmetries, we derive exact solution of the above-mentioned fractional ordinary differential equations wherever possible.

Description: The Bäcklund transformations and the superposition formulas of the Riccati equation with constant coefficients are constructed. Two fractional type solutions of the Riccati equation are obtained from its Bäcklund transformations. The equivalence relations between fractional solutions and previous known solutions are proved. A so-called unified Riccati equation expansion method for generating infinite number of exact traveling wave solutions for nonlinear evolution equations is then developed on the basis of the fractional solutions. With the method, infinitely many exact traveling wave solutions of two new classes of Benjamin–Bona–Mahony equations are presented.

Description: The nonlinear harmonic response of a cantilever hard-coating plate which is made of a layer of anisotropic hard-coating material and isotropic metal substrate is investigated based on the theory of high-order shear deformation of plate. Firstly, based on the theories of von Karman and Reddy’s three-order shear deformation, the nonlinear dynamic equations of hard-coating plate are built by Hamilton variation principle. Secondly, to obtain nonlinear governing equation of hard-coating plate under transverse load, these equations are discretized in Galerkin method. The system averaged equations with 1:3 internal resonances are obtained by the method of multiple scales, and the multi-periodic responses behavior of cantilever hard-coating plate under transverse loading could be presented. Finally, the vibration response experiment of hard-coating plate is conducted, and the multi-periodic responses are also present for the hard-coating plate with three-to-one internal resonance. Besides, through the vibration response experiment of uncoated titanium alloy plate, the damping characteristic of hard coating is further analyzed.

Description: In this paper, an intermittent control scheme is adopted to deal with the synchronization problem of fractional-order memristive neural networks(FMNNs) with switching jumps mismatch. Considering the inherent characteristic of FMNNs, a fractional-order differential inequality is introduced. Based on differential inclusions theory and the properties of Mittag Leffler function, some intermittent synchronization criteria are derived. The synchronization regain which is related to order \(\alpha \) , control period T and the control width \(\delta \) is discussed in details. In addition, the lag complete synchronization criteria of FMNNs with switching jumps match are also obtained by period intermittent control. Finally, numerical simulations are presented to verify the effectiveness of the theoretical analysis.

Description: This paper proposes an active disturbance rejection adaptive controller for tracking control of a class of uncertain nonlinear systems with consideration of both parametric uncertainties and uncertain nonlinearities by effectively integrating adaptive control with extended state observer via backstepping method. Parametric uncertainties are handled by the synthesized adaptive law and the remaining uncertainties are estimated by extended state observer and then compensated in a feedforward way. Moreover, both matched uncertainties and unmatched uncertainties can be estimated by constructing an extended state observer for each channel of the considered nonlinear plant. Since parametric uncertainties can be reduced by parameter adaptation, the learning burden of extended state observer is much reduced. Consequently, high-gain feedback is avoided and improved tracking performance can be expected. The proposed controller theoretically guarantees a prescribed transient tracking performance and final tracking accuracy in general while achieving asymptotic tracking when the uncertain nonlinearities are not time-variant. The motion control of a motor-driven robot manipulator is investigated as an application example with some suitable modifications and improvements, and comparative simulation results are obtained to verify the high tracking performance nature of the proposed control strategy.

Description: In this paper, we study quasi-periodic vibrational energy harvesting in a delayed self-excited oscillator with a delayed electromagnetic coupling. The energy harvester system consists in a delayed van der Pol oscillator with delay amplitude modulation coupled to a delayed electromagnetic coupling mechanism. It is assumed that time delay is inherently present in the mechanical subsystem of the harvester, while it is introduced in the electrical circuit to control and optimize the output power of the system. A double-step perturbation method is performed near a delay parametric resonance to approximate the quasi-periodic solutions of the harvester which are used to extract the quasi-periodic vibration-based power. The influence of the time delay introduced in the electromagnetic subsystem on the performance of the quasi-periodic vibration-based energy harvesting is examined. In particular, it is shown that for appropriate values of amplitudes and frequency of time delay the maximum output power of the harvester is not necessarily accompanied by the maximum amplitude of system response.

Description: We propose a time-delayed hyperchaotic system with a single-humped nonlinearity that can be implemented in a controlled way using off-the-shelf electronic circuit elements. The proposed system is simple in design yet complex in its dynamical behavior. A rigorous stability analysis reveals that the system gives birth to a limit cycle via a supercritical Hopf bifurcation and also theoretical analysis predicts the occurrence of higher periodic cycles with increasing time delay. The complexity of the system is characterized by phase plane plots, bifurcation diagram and Lyapunov exponent spectrum. The system is implemented in an electronic circuit, and a data acquisition system is used to control the relevant circuit parameter to visualize the experimental bifurcation diagram. Experimental observations qualitatively support the analytical and numerical results. We believe that the present study will improve our understanding of the dynamical behavior of time-delayed systems with single-humped nonlinearity, which are very much relevant in physiological systems.

Description: From the governing equation \(-(3+1)\) -dimensional nonlinear Schrödinger equation with cubic-quintic-septimal nonlinearities, different diffractions and \({\mathcal {PT}}\) -symmetric potentials, we obtain two kinds of analytical Gaussian-type light bullet solutions. The septimal nonlinear term has a strong impact on the formation of light bullets. The eigenvalue method and direct numerical simulation to analytical solutions imply that stable and unstable evolution of light bullets against white noise attributes to the coaction of cubic-quintic-septimal nonlinearities, dispersion, different diffractions and \({\mathcal {PT}}\) -symmetric potential.

Description: This paper investigates the adaptive fuzzy visual tracking control problem for telecontrolled manipulator system with input quantized by the proposed saturation switch quantizer (SSQ). Compared with the existing logarithmic quantizer and uniform quantizer, the major superiority of this newly SSQ lies in its adjustable communication rate and quantization density, simultaneously taking the input saturation effect into account. By establishing a nonlinear decomposition-based scheme for the output of SSQ, the control difficulty caused by discrete quantized input is overcome successfully. In addition, the requirement of visual velocity in controller construction is removed by introducing a visual velocity observer, and thus, large image noises and computational burden are both avoided. Subsequently, without the exact knowledge of robot dynamics, a novel adaptive fuzzy visual servoing controller is developed to guarantee the boundedness of closed-loop signals and the tracking performance. The effectiveness of the proposed adaptive fuzzy control scheme is confirmed by comparative simulations.

Description: In practice, overhead crane systems are widely used and the traditional control methods for a crane system usually treat it as a single pendulum system. However, when the hook mass cannot be ignored or the payload is too large, the crane system may behave more like a double pendulum system, which leads to the fact that traditional control methods are not suitable in this situation. In this paper, we focus on the control problem of a double pendulum crane system and propose a time-optimal trajectory planning method with the consideration of various constraints which can achieve the objectives of both accurate trolley positioning and double pendulum swing suppression. Specifically, the discrete system model is obtained using the discretization technique firstly. Then by deeply analyzing and considering a series of constraints, we formulate a quasiconvex optimization problem. After that, the bisection method is chosen to solve the obtained optimization problem with the corresponding time-optimal trajectory constructed conveniently. A tracking controller is also designed for the double pendulum crane system, which achieves proper trolley tracking performance. At last, both simulation and experimental results are included to illustrate the superior performance of the proposed trajectory planning method.

Description: The air spring component with a damper inside is widely used in the commercial vehicle as a vibration isolator. The nonlinear dynamics of the air spring component is important for full vehicle ride comfort evaluation. This paper aims to develop a mechanical model of the air spring component which can reproduce the air spring characteristics correctly. The proposed model consists of three split force branches in parallel describing the nonlinear elastic characteristics based on thermodynamics, the asymmetrical hysteresis and amplitude dependence by variable Berg’s friction, and the frequency dependency with four-parameter fractional derivative model. The air spring component bench tests are conducted, and the procedure of model parameter identification and model verification is presented. The nonlinear dynamic responses of the proposed model are investigated under a large amplitude excitation and different pre-compressions/pre-elongations by comparing with the Berg’s model which uses a linear elastic force element. Additionally, the proposed model and the Berg’s model for the air spring component are separately integrated into a full vehicle multibody dynamic model to evaluate the ride comfort as application for further verification through the co-simulation method using MATLAB/Simulink and MSC.ADAMS. The proposed model is verified to be more accurate than the Berg’s model through comparison with the full vehicle ride comfort test results.

Description: In this paper, we investigate nonlinear dynamical responses of two-degree-of-freedom airfoil (TDOFA) models driven by harmonic excitation under uncertain disturbance. Firstly, based on the deterministic airfoil models under the harmonic excitation, we introduce stochastic TDOFA models with the uncertain disturbance as Gaussian white noise. Subsequently, we consider the amplitude–frequency characteristic of deterministic airfoil models by the averaging method, and also the stochastic averaging method is applied to obtain the mean-square response of given stochastic TDOFA systems analytically. Then, we carry out numerical simulations to verify the effectiveness of the obtained analytic solution and the influence of harmonic force on the system response is studied. Finally, stochastic jump and bifurcation can be found through the random responses of system, and probability density function and time history diagrams can be obtained via Monte Carlo simulations directly to observe the stochastic jump and bifurcation. The results show that noise can induce the occurrence of stochastic jump and bifurcation, which will have a significant impact on the safety of aircraft.

Description: We consider anti-control of Hopf bifurcation for the Shimizu–Morioka system by using an explicit criterion. We first provide the two conditions for the existence of Hopf bifurcation, that is, eigenvalue assignment and transversality conditions, which could be formulated through the coefficients of characteristic equation, and the obtained conditions do not need to calculate the eigenvalue and eigenvalue’s derivatives. The center manifold theory and normal form reduction are utilized to derive the nonlinear gains for controlling the stability of the created limit circle. In addition, we further improve the computing formulas of amplitude and frequency of Hopf limit cycle. Numerical analysis also verifies the effectiveness of the proposed results.

Description: A practical synchronization approach is proposed for a class of fractional-order chaotic systems to realize perfect \(\delta \) -synchronization, and the nonlinear functions in the fractional-order chaotic systems are all polynomials. The \(\delta \) -synchronization scheme in this paper means that the origin in synchronization error system is stable. The reliability of \(\delta \) -synchronization has been confirmed on a class of fractional-order chaotic systems with detailed theoretical proof and discussion. Furthermore, the \(\delta \) -synchronization scheme for the fractional-order Lorenz chaotic system and the fractional-order Chua circuit is presented to demonstrate the effectiveness of the proposed method.

Description: The onset of spatiotemporal chaos in coupled map lattice (CML) with a new coupling scheme called accumulated CML is studied in this paper. A rigorous proof of the existence of chaos in the sense of Li–Yorke is presented. Also the range of the coupling strength in which global synchronization can be obtained is calculated by stability analysis of the synchronized state. Finally, the positivity of Lyapunov exponents confirms the existence of chaos.

Description: A distributed-order time- and Riesz space-fractional Schrödinger equation (DOT–RSFSE) is considered. Distributed-order derivatives indicate fractional derivatives that are integrated over the order of the differentiation within a given range. That is to say, the order of the time derivative ranges from zero to one. The space-fractional derivative is defined in the Riesz sense. In this paper, a new numerical approach is developed for simulating DOT–RSFSE. The main characteristic behind this approach is to investigate a space-time spectral approximation for spatial and temporal discretizations. Firstly, the given problem in one and two dimensions is transformed into a system of distributed-order fractional differential equations by using Jacobi–Gauss–Lobatto (J–G–L) collocation approach. Then, an efficient spectral method based on Jacobi–Gauss–Radau (J–G–R) collocation approach is applied to solve this system. Furthermore, the error of the approximate solution is theoretically estimated and numerically confirmed in both temporal and spatial discretizations. In order to highlight the effectiveness of our approaches, several numerical examples are given and compared with those reported in the literature.

Description: Nonlinear aeroelastic behavior of a trapezoidal wing in hypersonic flow is investigated. The aeroelastic governing equations are built by von Karman large deformation theory and the third-order piston theory. The Rayleigh–Ritz approach combined with the affine transformation is formulated and employed to transform the equations of a trapezoidal wing structure, modeled as a cantilevered wing-like plate, into modal coordinates. And then the modal equations are solved by numerical integrations. Several typical cases are studied to validate the capability of the proposed method for linear and nonlinear aeroelastic analysis of trapezoidal cantilever plate in hypersonic flow. The effects of Rayleigh–Ritz mode truncation for various wing-plate geometrical characteristics, i.e., sweep angle of leading edge, taper ratio and span, are examined to determine the appropriate mode number for accurate modeling and fast calculation. Meanwhile, the effects of various geometries of trapezoidal cantilever plates on the flutter stability are investigated. The nonlinear dynamic behaviors of the model with three typical geometries, namely, the rectangular, parallelogram and trapezoidal wing-like plate, are simulated numerically. Furthermore, complex dynamic behaviors are observed and identified via the phase plot, the Poincare map and the largest Lyapunov exponent. The results demonstrate that geometrical parameters of trapezoidal wing have significant effects on the nonlinear aeroelastic behaviors of wing structure. In particular, the evolution processes of chaos exhibit remarkable difference for these three wing configurations.

Description: The effects of colored noise, red noise and green noise, on the onset of chaos are investigated theoretically and confirmed numerically in the generalized Duffing system with a fractional-order deflection. Analytical predictions concerning the chaotic thresholds in the parameter space are derived by using the stochastic Melnikov method combined with the mean-square criterion. To qualitatively confirm the analytical results, numerical simulations obtained from the mean largest Lyapunov exponent are used as test beds. We show that colored noise can induce chaos, and the effects for the case of red noise on the onset of chaos differ from those for the case of green noise. The most noteworthy result of this work is the formula, which relates the chaotic thresholds among red, green and white noise, holds for noise-induced chaos in the Duffing system. We also show that Gaussian white noise can induce chaos more easily than colored noise.

Description: In the super-critical regime, steady-state responses of an axially moving beam are analyzed subjected to parametric combined with forced excitations. By employing the method of multiple scales, the primary resonance is investigated. Steady-state resonances exist unless the parametric frequency and the external frequency are commensurable. Natural modes are triggered when the parametric frequency is close to two times of or just the natural frequency. For the case of the first one, the combined excitation deduces a response curve with twin resonance peaks. Distance of them is determined by the parametric excitation, and the widths are depended on the external force. Double jumping is found in the response curve. For the case of the second one, the combined excitation produces a simple resonance in the form of a typical forced vibration. The response curve is superimposed by each of the excitations. With the numerical method, the incommensurability of excitation frequencies is found to produce beats and quasi-periodicity vibrations.

Description: Dielectric elastomer is a prosperous material in electromechanical systems because it can effectively transform electrical energy to mechanical work. In this paper, the period and periodic solution for a spherical dielectric elastomer balloon subjected to static pressure and voltage are derived through an analytical method, called the Newton–harmonic balance (NHB) method. The elastomeric spherical balloon is modeled as an autonomous nonlinear differential equation with general and negatively powered nonlinearities. The NHB method enables to linearize the governing equation prior to applying the harmonic balance method. Even for such a nonlinear system with negatively powered variable and non-classical non-odd nonlinearity, the NHB method is capable of deriving highly accurate approximate solutions. Several practical examples with different initial stretch ratios are solved to illustrate the dynamic inflation of elastomeric spherical balloons. When the initial amplitude is sufficiently large, the system will lose its stability. Comparison with Runge–Kutta numerical integration solutions is also presented and excellent agreement has been observed.

Description: Under investigation in this paper is a generalized (3 + 1)-dimensional variable-coefficient BKP equation, which can be used to describe the propagation of nonlinear waves in fluid mechanics and other fields. With the aid of binary Bell’s polynomials, an effective and straightforward method is presented to explicitly construct its bilinear representation with an auxiliary variable. Based on the bilinear formalism, the soliton solutions and multi-periodic wave solutions are well constructed. Furthermore, the tanh method and the tan method are employed to construct more traveling wave solutions of the equation. Finally, the asymptotic properties of the multi-periodic wave solutions are systematically analyzed to reveal the connection between periodic wave solutions and soliton solutions. It is interesting that the periodic waves tend to solitary waves under a limiting procedure. Our results can be used to enrich the dynamical behavior of higher-dimensional nonlinear wave fields.

Description: In this paper, a secure image transmission scheme based on synchronization of fractional-order discrete-time hyperchaotic systems is proposed. In this scheme, a fractional-order modified-Hénon map is considered as a transmitter, the system parameters and fractional orders are considered as secret keys. As a receiver, a step-by-step delayed observer is used, and based on this one, an exact synchronization is established. To make the transmission scheme secure, an encryption function is used to cipher the original information using a key stream obtained from the chaotic map sequences. Moreover, to further enhance the scheme security, the ciphered information is inserted by inclusion method in the chaotic map dynamics. The first contribution of this paper is to propose new results on the observability and the observability matching condition of nonlinear discrete-time fractional-order systems. To the best of our knowledge, these features have not been addressed in the literature. In the second contribution, the design of delayed discrete observer, based on fractional-order discrete-time hyperchaotic system, is proposed. The feasibility of this realization is demonstrated. Finally, different analysis are introduced to test the proposed scheme security. Simulation results are presented to highlight the performances of our method. These results show that, our scheme can resist different kinds of attacks and it exhibits good performance.

Description: In this paper, a nonlinear supported Euler–Bernoulli beam under harmonic excitation coupled to a 2 degree of freedom vehicle model with cubic nonlinear stiffness and damping is investigated. The equations of motion are derived by Newton’s law and discretized into a set of coupled second-order nonlinear differential equations via Galerkin’s method with cubic nonlinear terms. Based on the created model, numerical simulations have been conducted using the Runge–Kutta integration method to perform a parametric study on influences of the nonlinear support stiffness coefficient, mass ratio, excitation amplitude and position relation for the vehicle–bridge interaction (VBI) system by using bifurcation diagram and 3-D frequency spectrum. The results indicate that depending on different parameters, a diverse range of periodic motion, quasi-periodic response, chaotic behavior and jump discontinuous phenomenon are observed. And the chaotic regions are scattered between a number of periodic/quasi-periodic motions. The study may contribute to a further understanding of the dynamic characteristics and present useful information to dynamic design and vibration control for the VBI system.

Description: We made an attempt to provide a realistic picture of the localization of energy in microtubules (MTs), and we intend to model the nonlinear dynamics of MTs using the “double-well” \(\phi ^4\) form of the potential describing the dipole–dipole interactions. We investigate the modulational instability (MI) of the nonlinear plane wave solutions by considering both the wave vector ( q ) of the basic states and the wave vector ( Q ) of the perturbations as free parameters. A set of explicit criteria of MI is derived, and under the plane-wave perturbation, the constant amplitude solution becomes unstable and localized discrete breathers (DBs) solutions appear. We show numerically that MI is also an indicator of the presence of discrete breathers. We suggest that an electric field favourably leads the DB excitations towards the properly aligned end triggering a dissembly of the protofilament due to the energy release. These DBs could catalyse MT-associated proteins attachment/detachment and promote or inhibit the kinesin walk. We establish that the electromechanical vibrations in MTs can generate an electromagnetic field in the form of an electric pulse (breathers) which propagates along MT serving as signalling pathway in neuronal cells. The DBs in MT can be viewed as a bit of information whose propagation can be controlled by an electric filed. They might perform the role of elementary logic gates, thus implementing a subneuronal mode of computation. The generated DBs present us with novel possibilities for the direct interaction between the local electromagnetic field and the cytoskeletal structures in neurons. Thus, we emphasize that the effect of discreteness and electric field plays a significant role in MTs.

Description: Although chaotic systems with hidden attractors have been discovered recently, there is a few investigations about relationships among them. In this work, we introduce a unique simple chaotic flow which can belong to three famous categories of hidden attractors plus systems with self-excited attractors. This new system may help us in better understanding of chaotic attractors, especially hidden chaotic attractors.

Description: This paper investigates the generation of some novel bursting patterns in active control oscillator with multiple time delays. We present the bursting patterns, including symmetric codimension one and codimension two bursters with the slow variation of periodic excitation item. We calculate the bifurcation conditions of fast subsystem as well as its stability related to the time delay. We also identify some regimes of bursting depending on the magnitude of the delay itself and the strength of time delayed coupling in the model. Our results show that the dynamics of bursters in delayed system are quite different from those in systems without any delay. In particular, delay can be used as a tuning parameter to modulate dynamics of bursting corresponding to the different type. Furthermore, we use transformed phase space analysis to explore the evolution details of the delayed bursting behavior. Time delay can enhance the spiking performance and obtain the remarkable spiking dynamics even in a very simple model, which enriches the routes to bursting dynamics. Also some numerical simulations are included to illustrate the validity of our study.

Description: The properties of discrete breathers and modulational instability in a discrete \(\phi ^{4}\) nonlinear lattice which includes the next-nearest-neighbor coupling interaction are investigated analytically. By using the method of multiple scales combined with a quasi-discreteness approximation, we get a dark-type and a bright-type discrete breather solutions and analyze the existence conditions for such discrete breathers. It is found that the introduction of the next-nearest-neighbor coupling interactions will influence the existence condition for the bright discrete breather. Considering that the existence of bright discrete breather solutions is intimately linked to the modulational instability of plane waves, we will analytically study the regions of discrete modulational instability of plane carrier waves. It is shown that the shape of the region of modulational instability changes significantly when the strength of the next-nearest-neighbor coupling is sufficiently large. In addition, we calculate the instability growth rates of the \(q=\pi \) plane wave for different values of the strength of the next-nearest-neighbor coupling in order to better understand the appearance of the bright discrete breather.

Description: The active control approach generally requires power input to suppress vibrations of structures, while the conventional passive manner often causes waste of energy after transferring vibrations of the primary structure to the auxiliary system. In this work, an innovative control strategy based on energy harvesting for efficiently suppressing the cross-flow-induced vibrations such as galloping is proposed. The novel design facilitates the harvester of not only alleviating the oscillation of the primary structure but also seizing the transferred vibrational energy. An analytical model for the coupled nonlinear dynamical system is established by utilizing the Euler–Lagrange principle and implementing the Galerkin discretization. The impacts of the electrical load resistance and tip mass of the energy harvester on the coupled frequency, damping, and the onset speed of instability of the coupled multi-mode system are investigated in details. The results show that there exists an optimal load resistance for each tip mass which maximizes the onset speed of galloping. For control purposes, it is found that there is a well-defined tip mass of the energy harvester at which the coupled system has the highest onset speed of instability, and hence, the bluff body has the lowest vibration amplitude for all considered load resistances. However, to efficiently harvest energy and control the bluff body, both the tip mass of the energy harvester and electrical load resistance can be accurately determined.

Description: Analysis of piecewise-linear nonlinear dynamical systems is critical for a variety of civil, mechanical, and aerospace structures that contain gaps or prestress that are caused by cracks, delamination, joints or interfaces among components. Recently, a technique referred to as bilinear amplitude approximation (BAA) was developed to estimate the response of bilinear systems that have no gap or prestress. The method is based on an idea that the dynamics of a bilinear system can be treated as a combination of linear responses in two time intervals both of which the system behaves as a distinct linear system: (1) the open state and (2) the closed or sliding state. Both geometric and momentum constraints are then applied as compatibility conditions between the states to couple the linear vibrational response for each time interval. In order to estimate the response for more general cases where there are either gaps or prestress in the system, a generalized BAA method is proposed in this paper. The new method requires inclusion of contact stiffness and damping to model contact behavior in the sliding state, and new equilibrium positions for each state to establish proper coordinates. The new method also finds the bilinear frequency of the system, which cannot be computed using the bilinear frequency approximation method previously developed since that method is only accurate for the zero gap and no prestress case. The generalized BAA method is demonstrated on a single degree of freedom system, a three degree of freedom system, and a cracked cantilever beam model for various gap sizes and prestress levels.

Description: The paper studies periodic two-dimensional exclusion processes constituted by multi-lane totally asymmetric simple exclusion processes with the effect of asymmetric lane-changing rates. Particles in lane i can move forward with a rate \({p_i}\) or hop into the adjacent lane \({i-1}\) ( \({i+1}\) ) with a rate \(\omega _i^u\) ( \(\omega _i^d\) ). Complemented by Monte Carlo simulations, exact solutions have been derived. According to the detailed balance principle, two different cases \(\omega _{i - 1}^d = \omega _i^u\) and \(\omega _i^u = \omega _{i + 1}^d\) are studied here. Dynamics of the system can be revealed by exact solutions, which can match well with simulation ones.

Description: Considering how to exploit the lake resource reasonably, we propose a phytoplankton–fish model with the impulsive feedback control and investigate the sufficient conditions for the existence of the order-1 periodic solution by means of successor function. The stability of the order-1 periodic solution is discussed by a novel stability criterion on the basis of the stability theory of limit cycle. Furthermore, harvesting profit is maximized by using Pontryagin’s maximum principle subject to the impulsive feedback control. Finally, our results are justified by some numerical simulations.

Description: The chemical synapses in a neural network are known to be modulated by the neuronal firing activities through the spike-timing-dependent plasticity (STDP) rule. In this paper, we improve the multiplicative STDP rule by adding a momentum item with the aim of overcoming the low rate with which the neuronal network self-organizes into a stable complex structure. We find that the improved STDP rule with suitable momentum factors significantly speeds up the evolutionary process of the self-organized neuronal network. In addition, we explore the topological structure of self-organized neuronal network using complex network method. We show that the improved STDP rule generally results in a smaller node degree, clustering coefficient and modularity of self-organized neuronal network. Furthermore, we investigate the dynamical behaviors of self-organized neuronal network. We observe that depending on the momentum factor, the improved STDP rule has different effects on the network synchronization, neural information transmission, modularity and network complexity. Remarkably, for a specific momentum factor, the self-organized neuronal network shows the highest global efficiency of information transmission and the best combination between functional segregation and integration, which reflects the optimal dynamics as well as the topological structure. Our results provide a reasonable and efficient modulating rule of chemical synapse underlying the neuronal firing activities.

Description: This paper presents stability and bifurcations of two synaptically coupled identical Hindmarsh–Rose neurons with one time delay. The parameters we choose contribute to the single neuron exhibiting excitable behavior with a unique stable equilibrium. In the absence of time delay, we find coupling-induced oscillations, i.e., the excitable neurons can fire with different types of regular or irregular periodic spiking/bursting behaviors due to the synaptic coupling. With the help of stability and bifurcation theory, the asymptotic stability of equilibrium, fold and Hopf bifurcation are studied from the corresponding characteristic equation. In case of time delay, a detailed Hopf bifurcation analysis is given. And an explicit formula about the coupling strength and time delay for the occurrence of Hopf bifurcation is derived, based on which a series of periodic orbits generate when time delay passes through the critical value. Finally, numerical simulations are carried out for supporting our theoretical results; meanwhile, branches of Hopf bifurcation curves are plotted in the two-parameter plane.

Description: In this paper, we investigated the coupled nonlinear Schrödinger equations with arbitrary linear time-dependent potential, which govern the soliton dynamics in quasi-one-dimensional two-component Bose–Einstein condensates. Hirota method is developed carefully for applying into this model, and we obtain the exact nonautonomous superposition (NASP) N-soliton solutions analytically. Through manipulating the time-dependent potential, the different-type NASP solitons are reported. In particular, these new soliton solutions are the superposition of dark and bright solitons, so the general bright-bright and bright-dark (or dark-bright) soliton solutions can be obtained easily. A detailed analysis for the asymptotic behavior of solitons demonstrates that the interactions of S-type two solitons and periodic-type three solitons are all elastic in each component.

Description: This paper focuses on the exponential synchronization of nonlinearly coupled Markovian jumping complex dynamical networks with stochastic perturbations under delayed impulsive controller. The Markovian jumping parameters are represented as a continuous-time, finite-state Markov chain. The impulsive control law is defined with both distributed as well as discrete time-varying delays. By designing the efficient impulsive control strategy and by using the Lyapunov method and Ito’s formula, some simple and easily realized adequate conditions that assure the exponential synchronization of considered complex dynamical networks are derived in mean square sense. Finally, some simulation results are granted to display the effects of the theoretical findings.

Description: We call attention to a dual-pair concept for modeling hysteresis involving instantaneous switching: Specifically, there are two input–output pairs for each hysteresis model under one specific input, namely a differential pair and an integral pair. Currently in engineering mechanics, only one pair is being recognized and utilized, not the other. Whereas this dual-pair concept is inherent in the differential and algebraic forms of memristors and memcapacitors, the concept has not been carried over to memristive system theory, nor to memcapacitive system theory. We show that the “zero-crossing” feature in memristors, memcapacitors, and memristive/memcapacitive models (i.e., the “mem-models”) is also a feature of the differential pairs of well-known non-mem-models, examples of which are Ramberg–Osgood, Bouc–Wen, bilinear hysteresis, and classical Preisach. The dual-pair concept thus connects mem-models and non-mem-models, thereby facilitating the modeling of hysteresis, and raising a set of scientific questions for further studies that might not otherwise come to awareness.

Description: The study discusses the problem of determining vertical displacements of a riser’s ends, which, despite its horizontal displacements induced by waves, mitigate stresses. A spatial model of riser dynamics is presented that considers the geometric nonlinearity due to large deflections. The Rigid Finite Element Method was used for riser discretisation. Analyses are reported that enabled riser’s vibration frequency determination according to the positions of its upper and lower ends. Then a dynamic optimisation task was formulated and solved. It consists of the selection of riser’s vertical displacements that provide bending moments’ stabilisation at its selected points, tension forces, despite the defined horizontal movements of the riser’s upper end induced by waves. The calculations were performed for variable amplitudes of riser end’s horizontal movements.

Description: This paper is devoted to demonstrate how a class of fractional-order chaotic systems can be controlled in a given finite time using just a single control input. First a novel fractional switching sliding surface is proposed with desired properties such as fast convergence to zero equilibrium and no steady state errors. At the second phase, a smooth reaching control law is derived to guarantee the occurrence of the sliding motion with a finite settling time. Owing to the integration of the control signal discontinuity, chattering oscillations are hindered from the controller. Rigorous stability analysis is performed to validate the design claims. The effects of high frequency external noises as well as modeling errors and dynamic variations are also taken into account, and the robustness of the closed-loop system is ensured. The proposed robust controller is realized for a class of chaotic fractional-order systems with one control input. In accordance, some remarks regarding the inclusion of mismatched uncertainties in the system dynamics are given. The robust functionality and quick convergence property as well as chatter-free attribute of the introduced non-smooth sliding mode technology are demonstrated using oscillation suppression of fractional-order chaotic Lorenz and financial systems.

Description: In this paper, new planar isoparametric triangular finite elements (FE) based on the absolute nodal coordinate formulation (ANCF) are developed. The proposed ANCF elements have six coordinates per node: two position coordinates that define the absolute position vector of the node and four gradient coordinates that define vectors tangent to coordinate lines (parameters) at the same node. To shed light on the importance of the element geometry and to facilitate the development of some of the new elements presented in this paper, two different parametric definitions of the gradient vectors are used. The first parametrization, called area parameterization, is based on coordinate lines along the sides of the element in the reference configuration, while the second parameterization, called Cartesian parameterization, employs coordinate lines defined along the axes of the structure (body) coordinate system. The fundamental differences between the ANCF parameterizations used in this investigation and the parametrizations used for conventional finite elements are highlighted. The Cartesian parameterization serves as a unique standard for the triangular FE assembly. To this end, a transformation matrix that defines the relationship between the area and the Cartesian parameterizations is introduced for each element in order to allow for the use of standard FE assembly procedure and define the structure (body) inertia and elastic forces. Using Bezier geometry and a linear mapping, cubic displacement fields of the new ANCF triangular elements are systematically developed. Specifically, two new ANCF triangular finite elements are developed in this investigation, namely four-node mixed-coordinate and three-node ANCF triangles. The performance of the proposed new ANCF elements is evaluated by comparison with the conventional linear and quadratic triangular elements as well as previously developed ANCF rectangular and triangular elements. The results obtained in this investigation show that in the case of small and large deformations as well as finite rotations, all the elements considered can produce correct results, which are in a good agreement if appropriate mesh sizes are used.

Description: Under the relaxed triangular-type condition on the drift terms and diffusion terms, this paper investigates the problem of the fourth moment exponentially stable for a class of stochastic nonlinear systems by, respectively, adopting state feedback and output feedback. Based on the Lyapunov stability criterion, the parameter-dependent controller, which is used to compensate for the drift terms and diffusion terms, is constructed such that the closed-loop system is fourth moment exponentially stable. Furthermore, the fourth moment exponential stability of the system states and errors can be guaranteed. Two simulation examples are provided to demonstrate the effectiveness of the proposed design scheme.

Description: We investigate generalized stochastic resonance (GSR) in a fractional harmonic oscillator with time delay and fluctuation damping. Considering that nonlinear noise widely exists in actual systems compared with linear noise, the fluctuation of damping is modeled as polynomial trichotomous noise. The analytical expression of the output amplitude gain is derived by applying small delay approximation and stochastic averaging. Simulation results show that the output amplitude gain curves, as functions of time delay versus noise parameters, behave non-monotonically and exhibit typical GSR. Furthermore, nonlinear phenomena of stochastic multi-resonance with two, three, and four peaks are observed. Finally, we provide the phase diagrams for GSR versus time delay with different system parameters. Furthermore, the mechanism underlying the stochastic multi-resonance with two, three, and four peaks, as well as their connections, is elucidated. This study could serve as a theoretical basis for the practical use and control of GSR in future works.

Description: In this work, a time-varying stiffness method is proposed for extracting highly accurate approximation for the fundamental backbone branches of the frequency–energy plot from the numerical simulation response of the nonlinear dynamical system. The purely nonlinear duffing oscillator with a nonnegative real power restoring force is firstly considered to develop the method, and later the method is applied to linear systems attached with a nonlinear energy sink for more demonstration. The systems of concern are numerically simulated at an arbitrary high level of initial input energy to apply the proposed method. Accordingly, the obtained responses of these systems are employed via the proposed time-varying stiffness method to extract an approximation for the fundamental backbone branches in the frequency–energy plot. The obtained backbones have been found in excellent agreement with the exact backbones of the considered systems. Even though these approximate backbones have been obtained for only one high energy level, they are valid for any other initial energy below that level. In addition, they are not affected by the damping variations in the considered systems. The proposed method is found to be applicable to well approximate the fundamental backbone branches of the large-scale nonlinear dynamical systems. The frequency–amplitude dependences have been also studied here for the considered systems.

Description: This paper studies synchronization in a multi-agent system, which is defined as a situation where all the agents in a group are required to achieve a common velocity direction. The agents are assumed to be coupled through controller gains that are not necessarily identical or homogeneous, which addresses a practical scenario where the gains may vary nominally due to minor implementation errors or drastically due to major faults or errors. The paper analyzes the effect of heterogeneous gains on the common velocity direction at which the system of agents synchronizes. Conditions under which heterogeneous controller gains result in a synchronized formation are derived and it is shown that the resulting common velocity direction lies in the conic hull of the initial velocity vectors of agents. A detailed analysis of the two agents system shows that there exists a less restrictive condition on heterogeneous gains that results in synchronization. Effect of saturation is also studied for two cases when the controller gains are bounded and when the control efforts are bounded. Both all-to-all and limited communication topologies are considered. Simulations are given to support the theoretical findings.

Description: The influence of blade vibration on the nonlinear characteristics of rotor–bearing system is non-ignorable in estimating system performance. The extensive studies simplify the rotor system as lumped mass points. The influence of shaft’s bending and shear and the flexibility are usually ignored. The present paper is aim to analyze the nonlinear dynamic behavior of a continuum model. The continuum model of flexible blade–rotor–bearing coupling system is established, simplifying the shaft as Timoshenko beam. The Lagrange method is utilized to derive the differential equation of motion of system. Then, the nonlinear equations of coupling system are numerically solved using the Newmark- \(\upbeta \) method. The results obtained through the proposed model are compared with the rotor–bearing system without the blades. The effect of several parameters such as rotational speed, the damping coefficient and the length of blade on the nonlinear dynamics of rotor system have been investigated. Inclusive of the analysis methods of bifurcation diagram, three-dimensional spectral plots, time-base analysis, Poincare maps and spectral plots are used to analyze the behavior of the coupling system under different operating conditions, which exhibits rich dynamic behavior of the system.

Description: This paper proposes a nonlinear controller for a quadrotor helicopter, under the control of which the system is globally asymptotically stabilized with good control quality. The proposed controller is synthesized by Command Filtered Backstepping method with a novel parameter scheduling scheme. By scheduling controller parameters within the system-stabilizing region, the convergence speeds of errors in each step are adaptively adjusted based on different flight conditions. Amplitudes of control signals are reduced during fast tracking progress to avoid actuator saturation, which is hardly modeled and may cause instability. The controller also allows more aggressive tuning that achieves better regulation accuracy. The technology to implement the proposed controller is illustrated in detail, and key parameters of quadrotor model and the actuator’s dynamics are identified by experiments. To validate the proposed method, experimental flight tests are conducted under three typical flight conditions. Results comparing to other methods such as PID, sliding mode control and dynamic surface control are demonstrated, showing that the proposed controller is practical to an actual quadrotor system and can achieve good control performance.

Description: In this paper, we first verify that fractional order systems using Caputo’s or Riemann–Liouville’s derivative can be represented by the continuous frequency distributed model with initial value carefully allocated. Then, the relation of the stability between the fractional order system and its corresponding integer order system is discussed and it is proven that stability of integer order system implies the stability of its corresponding fractional order system under some mild conditions. Moreover, we extend the stability theorems to the finite-dimensional case since fractional order systems are always implemented by approximation. Some illustrative examples are finally provided to show the usage and effectiveness of the proposed stability theorems.

Description: We present a new approach based on the modeling of the behavior of the number of ordinal matrices derived from time series, as a function of the embedding dimension. We show that the number of distinct ordinal matrices can be used for determining whether the dynamics are regular or chaotic by means of the periodicity ( \(\mu \) ), quasiperiodicity ( \(\alpha \) ) and nonregularity ( \(\lambda \) ) index herein defined. We verify that \(\lambda \) behaves similarly to the Lyapunov exponent and therefore can be used for measuring complexity in time series whose underlying equations are unknown. Moreover, the combination of \(\mu \) , \(\alpha \) and \(\lambda \) enables us to distinguish between deterministic and stochastic data. We thus propose the variation law of the number of ordinal matrices characterizing the random walk.

Description: This article is interested in presenting and implementing two new numerical algorithms for solving multi-term fractional differential equations. The idea behind the proposed algorithms is based on establishing a novel operational matrix of fractional-order differentiation of generalized Lucas polynomials in the Caputo sense. This operational matrix serves as a powerful tool for obtaining the desired numerical solutions. The resulting solutions are spectral, and they are built on utilizing tau and collocation methods. A new treatment of convergence and error analysis of the suggested generalized Lucas expansion is presented. The presented numerical results demonstrate the efficiency, applicability and high accuracy of the proposed algorithms.

Description: This paper puts forward a new nonlinear adaptive controller for a small-scale unmanned helicopter with unknown mass. The controller is developed under the framework of backstepping technique, with the unknown mass estimated by a novel identifier and the internal and external uncertainties approximated by radial basis function neural networks (RBFNNs). The overall closed-loop system, which consists of three parts: longitudinal–lateral subsystem, heave subsystem, and heading subsystem, is proved to be semi-globally uniformly ultimately bounded by the strict Lyapunov stability theory. Furthermore, the proposed method is more practical in actual applications with an improved online learning algorithm of the least parameters used in the RBFNNs. Finally, the effectiveness and the robustness of the proposed strategy are exhibited through two simulations compared with the classic PID method.

Description: In this paper, a robust adaptive self-organizing neuro-fuzzy control (RASNFC) scheme for tracking of unmanned underwater vehicle with uncertainties and the unknown dead-zone nonlinearity is proposed. The proposed RASNFC scheme comprises an estimation-based adaptive controller (EBAC) using a self-organizing neuro-fuzzy network (SNFN) and a robust controller. The EBAC controller is constructed with a novel sliding mode reaching law control framework, and the unknown dynamic function is identified by the SNFN approximator which is able to online self-construct a neuro-fuzzy network with dynamic structure by generating and pruning fuzzy rule. The robust controller is employed to provide the finite \(L_{2}\) -gain property to cope with reconstruction errors such that the robustness of the entire closed-loop control system is enhanced. Theoretical analysis shows that tracking errors and their derivatives are asymptotically stable and all signals in the closed-loop system are bounded. Comparative simulation results demonstrate the effectiveness and superiority of the proposed RASNFC scheme.

Description: The article presents authors’ recent results on nonlinear lateral stability of rail vehicles in a curved track. The theories of self-exciting vibrations and bifurcation are the key elements here. The general objective is presentation of extended use of the earlier worked out authors’ method to more complex rail vehicle models. Two 4-axle vehicle models were created. The first one represents coach MKIII described with multibody software by the first author. The second one represents coach 127A described with use of engineering multibody software VI-Rail. The models are described, and method of the analysis is shortly reminded. Then, results for both models are presented. They include verification of the limit cycle possible passage from straight track to circular curve and stability maps for regular curves of different radii and straight track. Next influence of selected suspension parameter and wheel–rail coefficient of friction on vehicle stability is shown. The more general objective is the authors’ say in the hot polemics on the advisability of rail vehicle stability analysis in curves and on the advantages of the nonlinear methods of such analysis over the linear ones.

Description: In this paper, we propose and analyze a new descriptive model of armed conflicts among N groups. The model is composed of \(N^2\) ordinary differential equations, with \(3(N^2+N)\) constant parameters that describe military characteristics and recruitment policies, ranging from pure defensivism to pure fanaticism. The results are only preliminary, but point out interesting (though not very surprising) properties: periodic coexistence is possible, and multiple attractors can exist; governmental groups cannot go extinct if they are highly defensivist, and rebels cannot be eradicated if they are highly fanatic. Shocks due to interventions of short duration of an external army can stabilize/destabilize the system and/or eradicate some group, and the same holds true for small structural changes. Other more subtle questions concerning, for example, the existence of chaotic regimes and the systematic evaluation of the role of strategic factors like power, intelligence, and fanaticism, remain open and require further research.

Description: This paper presents an investigation on anomalous diffusion of cells in a two-dimensional comb framework with effects of fractional Cattaneo flux. Formulated governing equation is an evolution equation with the coexisting characteristics of parabolic (diffusion) and hyperbolic (wave) for \(\alpha \) in (0, 1). Exact solution is obtained by the special fractional integral transformations, and a novel invariant is established, i.e., \(\left\langle {x^{2}\left( t \right) } \right\rangle \cdot \left\langle P \right\rangle = 0.5\) (the mean square displacement multiplied by the total number of cells along the x -axis = 0.5). Moreover, the characteristics of cells distribution, the total number and the mean square displacement of cells along the x -axis with different involved parameters, especially with the fractional parameter evolution, are shown graphically and analyzed in detail. For the cells distribution versus x , it turns from parabolic and hyperbolic with the decrease in t or the increase in \(\alpha \) or \(\xi \) . It is monotonically decreasing for the cells distribution versus \(\alpha \) with different x , t and \(\xi \) . For the distribution versus t with different \(\alpha \) and \(\xi \) or versus \(\alpha \) with different t , it is monotonically decreasing for the distribution of total number while monotonically increasing for the distribution of mean square displacement. It is remarkable that the anomalous subdiffusion happens along the x -axis for arbitrary parameters which is different from the classical Cattaneo diffusion.