Several Classes Of Chaotic Synchronization Via Impulsive Control

In the past few decades, chaos synchronization has been become a hot topic of the nonlinear sciences due to its great potential application in the field of physical systems, ecological networks and secure communications, etc, which has attracted much attention from a wide range of domestic and overseas scientists and engineers, since the pioneering work of American scalar Pecora and Carroll. Chaos synchro-nization means the dynamic trajectory of one system converge to another system’s trajectory so that the trajectory of two systems keeps pace in the later time. The aim of chaos synchronization is that the response systems with any initial conditions recover the given chaotic trajectory from the drive system. In this paper, we inves-tigate several classes of chaos synchronization:function projective synchronization, the increasing-order synchronization of chaotic system and lag synchronization via impulsive control, and the structure is as follow:In Chapter l,we introduce the base theory of chaos synchronization and the chief content of this paper.In Chapter2,we give the definition of function projective synchronization, and investigate nonlinear adaptive-impulsive function projective synchronization of chaotic systems.The core of nonlinear adaptive-impulsive function projective syn-chronization of chaotic systems is to design the suitable nonlinear adaptive-impulsive controllers to attain certain aim.Based on invariant principle of impulsive dynami-cal systems,it has been shown that the function projective synchronization can be realized by nonlinear adaptive-impulsive control.In Chapter3,the synchronization of two different order chaotic systems has been investigated via impulsive control. Based on of impulsive functional differen-tial equation, sufficient conditions guaranteed the error dynamics is asymptotically stable and convergent to a predetermined level.Computer simulations are presented to verify the theoretical results.In Chapter4,we proposed a unified for impulsive lag-synchronization of chaotic and hyperchaoic systems with time delay by employing the stability theory of im-pulsive delayed differential equation.The delayed lorenz system and are presented to illustrate the effectiveness of our...