Generalized Synchronization Of Non-identical Chaotic Systems

Nonlinear science is a foundational discipline which concerns the common properties of nonlinear phenomena. Particularly, Chaos theory is one of important subdiscipline of nonlinear science. Based on the theory analysis and numerical simulations, the research has studied the generalized synchronization of non-identical chaos systems. The main originality in this paper can be summarized as follows:(1) The synchronization problem of a new chaotic system is studied. Three different methods, linear feedback method, nonlinear feedback method and impulsive control method are used to control synchronization of the new chaotic systems. Based on the Lyapunov stability theory and impulsive control technology, the conditions of synchronization are discussed, and they are also proved theoretically. Numerical simulations show the effectiveness of the three different methods.(2) GS of diverse structure discrete-time chaotic systems is investigated. Based on the Lyapunov stability theory, an effective scheme to realize GS for two diverse structure discrete-time chaotic systems is proposed. By theory analysis, two diverse structure discrete-time chaotic systems can be achieved GS via choose reasonable feedback gain matrix. Numerical simulations are given to show the effectiveness of the proposed approach.(3) A generalized (lag, anticipated, and complete) projective synchronization for a general class of chaotic systems is defined. A systematic, powerful and concrete scheme is developed to investigate the generalized (lag, anticipated, and complete) projective synchronization between the drive system and response system based on the adaptive control method and feedback control approach. The hyperchaotic Chen system and hyperchaotic Lorenz system are chosen to illustrate the proposed scheme. Numerical simulations are provided to show the effectiveness of the proposed schemes. In addition, the scheme can be also extended to research generalized (lag, anticipated, and complete) projective synchronization between non-identical discrete-time chaotic systems.(4) Controlling multi-scroll chaotic attractors from saturated function series is studied. For many chaotic systems that can be decomposed into a sum of a linear and nonlinear part, under some mild conditions the fuzzy neural networks (FNNs) can be used to well approximate the nonlinear part of the system dynamics. The resulting system is then dominated by the linear part, with some small or weak residual nonlinearity due to the FNNs approximation errors. Thus, a simple linear state feedback controller can be proposed, to drive the multi-scroll chaotic attractors to the desired targets or periodic trajectory. In addition to some theoretical analysis, computer simulations on multi-scroll chaotic attractors are presented to demonstrate the effectiveness of the proposed control scheme.