Study On Synchronization Methods Of Continuous Chaotic System

Chaos is a kind of special type in the nonlinear dynamical system, it is existed widely in nature. Recently, the control and synchronization of chaotic system have obtained rapid development. Chaos penetrates mutually with other many scientific domains, and becomes to an active research subject of the nonlinear domain. So it promise to have a huge application prospect. This thesis mainly focuses on the generalized synchronization, coupled synchronization and anti-synchronization of chaotic system. The main content is depicted as follows:Firstly, control and synchronization of chaotic system in the reseach background and study conditions are introduced. Then it gives the introduction of the basic correlative control theory in chaotic dynamical system, so it paves way for the later research.The generalized synchronization for a class of chaotic systems with unknown parameters is proposed. Based on Lyapunov stability theory and adaptive control method, the expressions of the adaptive controller and the updating rule of parameters are given. A new chaotic systems is taken as an example to realize the generalized synchronization and parameter identification.An active sliding mode controller is designed to anti-synchronization for a kind of continuous chaotic systems. The closed loop dynamic error depends on the linear part of the response systems and parameters of the controller. Therefore, the anti-sychonization rate can be adjusted through these parameters. This method may realize the anti-synchronization quickly. Analysis of the stability for the proposed method is done based on the Lyapunov stability theorem.At last, we discuss the synchronization of two linearly bidirectional coupled chaotic system .This synchronous controller is based on adaptive control theory. Appropriate coupling coefficient is derived by the Lyapunov stability theorem and a minimum scheme. The proposed scheme requires no concrete range of coupling coefficient and upper bound of trajectories of the coupled chaotic system.