Researches On Synchronization Of Chaotic Systems And Chaotification Of Non-Chaotic Systems

Chaos control has attracted more and more attention in the current research fields. Two important directions in chaos control are synchronization of chaotic systems and chaotification of non-chaotic systems. They are also the main contents in this dissertation. We focus on the synchronization of chaotic systems and the chaotification of time-continuous non-chaotic systems. The main research work is as follows:1 The impulsive synchronization of chaotic systems has attracted increasing attention in many chaos synchronization methods and some achievements have been made on impulsive synchronization. But most of them have complex controllers' structure or can only be used in some special chaotic systems. It is valuable to find out a method with simple controllers' structure that can be adapted to a wide class of chaotic systems. In this thesis, the problem of impulsive synchronization of a class of chaotic systems is concerned. First, an impulsive synchronization method for chaotic systems without uncertain parameters and channel time-delay is studied. Then an impulsive synchronization method for chaotic systems with channel time-delay is explored. Finally, an impulsive synchronization method for chaotic systems with uncertain parameters is discussed. Based on Lyapunov stability theory, two criterions are respectively developed to guarantee the global asymptotical synchronization of the two chaotic systems in each case mentioned above. The proposed method is simple, easy to implement and can be used in quite a lot of systems.2 Lorenz system, Chen system and Lu system are three different kinds of chaotic systems. These systems represent different types of chaotic motion. They are frequently used as classical chaotic models to study chaos control and chaos synchronization. It is a significant theme to build a new and widely used chaos model including the above three chaotic systems and even other chaotic systems, and develop a general method of chaos control and chaos synchronization for the new chaos model. Based on what have been mentioned above, a new chaos model with three parameters is first put forward, which includes Lorenz system, Chen system and Lu system. For this new chaos model, some synchronization methods employing only a single controller are respectively discussed in following three situations: the linear feedback synchronization for chaotic systems with identical and known parameters, the adaptive feedback synchronization for chaotic systems with identical but unknown parameters and the adaptive feedback synchronization for chaotic systems with non-identical and unknown parameters. The sufficient...