Nonlinear Dynamical Systems Chaos Synchronization

Chaos, as one of the important parts of the nonlinear science, is very popular. The synchronization of chaotic systems has been the research hotspots of nonlinear science for recent years and becomes the essential point in secure communication. Form the point of practical application, in this paper, we study chaos synchronization of complex Duffing system, lag synchronization of chaotic system with unknown parameters and generalized synchronization of different order of chaotic systems with unknown parameters. The work of this thesis is presented as follow:Chapter one introduces briefly the history and the current developments of the chaos theory. Then one focuses on the investigation history, current situations of chaos synchronization, the methods and types of chaos synchronization. At last, the elementary knowledge used in this dissertation and the main contents are given.In chapter two, we use Backstepping design technique to study the chaos synchronization of complex Duffing system. Theory analysis and numerical simulations confirm the validity and feasibility of the proposed method for complex Duffing system.In chapter three, we study generalized chaos synchronization of different order of chaotic systems with unknown parameters. Using add-order method to translate the problem of generalized synchronization of different order of chaotic systems into the identical order of chaotic systems. Then combining adaptive control method, we achieve generalized synchronization of different order of chaotic systems with unknown parameters and make all of the parameters of drive system and response system to be estimated. Numerical simulation demonstrates the effective of this method.In chapter four, the problem of lag synchronization of chaotic system with unknown parameters is proposed. Based on Lyapunov stability theory, lag controller and update law of parameters are obtained, then achieving the synchronization between drive system and response system. Numerical simulation demonstrates the robustness against the effective of bounded noise of the proposed control strategy.Chapter five concludes the work and points out some aspects to be further studied on chaos synchronization of nonlinear dynamic systems.