Research On Schemes Of Generalized Synchronization And Phase Synchronization Of Typical 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. The research studies the generalized synchronization and phase synchronization of chaos using the methods of theoretical derivation and numerical simulation. The main originality in this paper can be summarized as follows:(1) The generalized synchronization of chaos is studied, and a new method, by which adaptive generalized synchronization of chaotic systems with a kind of linear and nonlinear relationship between the drive and response systems can be achieved, is proposed. Based on the Lyapunov stability theory and Barbalat Lemma, the correctness of the proposed scheme is strictly demonstrated. Numerical simulations show the effectiveness of this method.(2) The author investigates the generalized synchronization and parameters identification of a class of uncertain chaotic systems. Based on the invariance principle of differential equations, a systematic method of adaptive control is developed. With this method parameters identification and generalized synchronization of chaotic systems can be achieved simultaneously. Numerical simulations show the effectiveness of the adaptive controller.(3) The generalized synchronization of different chaotic systems with partially unknown parameters is researched. By designing appropriate adaptive controller and parameter update law, the generalized synchronization and parameters estimation can be realized simultaneously. This scheme is not only for chaotic systems with the same dimensions but also for chaotic systems with different dimensions.(4) The author studies the phase synchronization of chaos. Based on the active control technique, an appropriate controller is designed to achieve the phase synchronization of chaotic systems. This method is applied to hyperchaotic Rossler system and another hperchaotic system (we call it vD system), respectively. Phase synchronization is also obtained between the two systems mentioned above. Numerical simulations further demonstrate the feasibility of the proposed scheme.