Synchronization Of Chaotic Impulsive Delay System

There are lots of chaos phenomena in real word. Knowledge on chaos is one of important achievements in nonlinear science. With the further research of chaos, chaos control and synchronization becomes an advanced research field. In this thesis, the problem of the chaos synchronization and with impulsive synchronization of delay chaotic systems is studied deeply and widely. The detail is clarified as follows:Firstly of all, the dissertation discusses systematically basic concepts of chaos: definition, main feature, the way to chaos and the significance and the respect of chaos are investigated briefly. After that we introduce some elementary theories: Lyapunov exponent reflectioning chaos dynamics characteristic, research chaotic system synchronization needs the structure Lyapunov function, Lyapunov stability theory and so on.Chaotic synchronization is refers to a system the orbit to converges to another system orbit, and continuously will maintain marches in step. Since Pecora and the Carroll foundation proposed and has realized driving-response synchronization, chaotic synchronization in the communication, electronics and so on in many domains has the huge application potential and the prospects for development.Third chapter, we first introduce the development of chaotic synchronization and its definition, our main aim is to establish foundation in order to research chaotic synchronization systematically and profoundly. Then we discuss chaotic the synchro-Nization each method to conduct the thorough research: Pceora-Carroll synchrozization, driving-response synchronization, feedback synchronization, self-adapt synchronization, observer synchronization method, neural network control method and so on. Because time delay and impulsive are possibly can affect the estimate synchronization results defeat factor, therefore the delay chaotic system synchronization question will be research in the third chapter, in view of a concrete delay chaotic system, gives in the foundation which the predecessor studied to promote, we have some conclusions of many delay chaotic systems synchronization. At present all yields some results of delay chaotic system synchronization or the impulsive chaotic system synchronization research, but impulsive synchronization of delay chaotic systems are not widespread. Therefore finally we on the basis of the predecessor achievement to research impulsive delay chaotic system synchronization.First we introduce impulsive synchronization, impulsive control, is the same with the above method, the use synchronization error feedback method, structure suitable the Lyapunov function analysis the system. We obtain some sufficient conditions and corollaries of impulsive delay chaotic system synchronization.