Xiangyong Chen

Hybrid synchronization behavior in an array of coupled chaotic systems with ring connection

In this paper, we investigate the hybrid synchronization behavior in an array of coupled chaotic systems with ring connection, of which means complete synchronization (CS) and anti-synchronization (AS) could coexist. First, the anti-synchronization controllers are designed, which can transform the synchronization error dynamic system into a nonlinear system with an antisymmetric structure. Second, we investigate the complete synchronization behavior in such a chaotic system under the anti-synchronization control. After that, the stability conditions are given for reaching hybrid synchronization. Finally, numerical examples and simulation results are presented to verify and validate the hybrid synchronization behavior in coupled chaotic system. HighlightsWe study the hybrid synchronization of multiple coupled chaotic systems with ring connection.In our chaotic systems model, we can avoid the occurrence of a fault to reach the synchronization.The new stability conditions are given for reaching hybrid synchronization.The controller designed can transform the synchronization error system as a simple nonlinear system.Research results will undoubtedly improve the performance of multilateral communications.

Finite-time multi-switching synchronization behavior for multiple chaotic systems with network transmission mode

Abstract By considering network transmission mode, this paper addresses the finite-time multi-switching synchronization problem for two kinds of multiple chaotic systems. For multiple same-order chaotic systems, we construct the general switching rules and analyze the existence of switching cases. The presented schemes guarantee the states of each derive system to be finite-timely synchronized with the desired states of every respond system in the different transmission paths and switching sequences. For multiple different order chaotic systems, we analyze a special multi-switching hybrid synchronization behavior, where part of the states are completely synchronized and the others belong to combination synchronization. Moveover, the easily verifiable criterion is derived for such synchronization. Finally, numerical examples are given to show the effectiveness of the presented theoretical results.

Existence and stability of periodic solution of high-order discrete-time Cohen–Grossberg neural networks with varying delays

Abstract This paper studies the existence and stability of periodic solution of the high-order discrete-time Cohen–Grossberg neural networks with varying delays. The properties of M-matrix and the contracting mapping principle are used to obtain a sufficient condition that guarantees the uniqueness and global exponential stability of the periodic solution. In addition, a numerical example is given that demonstrates the effectiveness of the proposed theoretical results.

Synchronization of Coupled Chaotic Systems with Ring Connection Based on Special Antisymmetric Structure

This paper considers the complete synchronization problem for coupled chaotic systems with ring connections. First, we use a direct design method to design a synchronization controller. It transforms the error system into a stable system with special antisymmetric structure. And then, we get some simple stability criteria of achieving the complete synchronization. These criteria are not only easily verified but also improve and generalize previous known results. Finally, numerical examples are provided to demonstrate the effectiveness of the theoretical analysis.

Finite-Time Control of Multiple Different-Order Chaotic Systems with Two Network Synchronization Modes

This paper mainly investigates finite-time synchronization of multiple different-order chaotic systems. Two kinds of different network synchronization modes are considered here, and the definitions of finite-time synchronization errors are given for such systems by constructing the proper vectors mapping functions. On the basis of finite-time control idea, the synchronization schemes are developed to ensure the asymptotical stability of two classes of different error systems in finite-time. Afterward, two numerical examples are calculated and simulated to illustrate the effectiveness and feasibility of proposed strategies.

Finite-time stability of genetic regulatory networks with impulsive effects

We study the finite-time stability of genetic regulatory networks with impulsive effects. Using the method of Lyapunov function, sufficient conditions of the finite-stability, in terms of linear matrix inequalities, are established. A numerical example is provided to further illustrate the significance of our results.

Robust Exponential Synchronization for a Class of Master-Slave Distributed Parameter Systems with Spatially Variable Coefficients and Nonlinear Perturbation

This paper addresses the exponential synchronization problem of a class of master-slave distributed parameter systems (DPSs) with spatially variable coefficients and spatiotemporally variable nonlinear perturbation, modeled by a couple of semilinear parabolic partial differential equations (PDEs). With a locally Lipschitz constraint, the perturbation is a continuous function of time, space, and system state. Firstly, a sufficient condition for the robust exponential synchronization of the unforced semilinear master-slave PDE systems is investigated for all admissible nonlinear perturbations. Secondly, a robust distributed proportional-spatial derivative (P-sD) state feedback controller is desired such that the closed-loop master-slave PDE systems achieve exponential synchronization. Using Lyapunov’s direct method and the technique of integration by parts, the main results of this paper are presented in terms of spatial differential linear matrix inequalities (SDLMIs). Finally, two numerical examples are provided to show the effectiveness of the proposed methods applied to the robust exponential synchronization problem of master-slave PDE systems with nonlinear perturbation.

Transmission Synchronization Control of Multiple Non-identical Coupled Chaotic Systems

In this paper, we investigate the transmission projective synchronization control problem for multiple, non-identical, coupled chaotic systems. By considering the influence of the occurrence of a fault between a driving system and a responding system, we define our new transmission synchronization scheme. After that, control laws are designed to achieve transmission projective synchronization and a simple stability criteria is obtained for reaching the transmission synchronization among multi-systems. A numerical example is used to verify the effectiveness of the synchronization within a desired scaling factor.

Stability and stabilization of a delayed PIDE system via SPID control

This paper addresses the problem of exponential stability and stabilization for a class of delayed distributed parameter systems, which is modeled by partial integro-differential equations (PIDEs). By employing the vector-valued Wirtinger’s inequality, the sufficient condition of exponential stability of the PIDE system with a given decay rate is investigated. The condition is presented by linear matrix inequality (LMIs). After that, we develop a spatial proportional-integral-derivative state-feedback controller that ensures the exponential stabilization of the PIDE system in terms of LMIs. Finally, numerical examples are presented to verify the effectiveness of the proposed theoretical results.

Dynamic analysis of periodic solution for high-order discrete-time Cohen-Grossberg neural networks with time delays

In this paper, we analyze the dynamic behavior of periodic solution for the high-order discrete-time Cohen-Grossberg neural networks (CGNNs) with time delays. First, the existence is studied based on the continuation theorem of coincidence degree theory and Youngs inequality. And then, the criterion for the global exponential stability is given using Lyapunov method. Finally, simulation result shows the effectiveness of our proposed criterion.