Pulse Delay Chaotic System Synchronization Problems

The chaos is a unique movement form of the non-linear dynamics system. It widely exists in the nature. Such as physics, chemistry, biology, geology as well as technical science, social sciences and so on each kind of scientific fields. The purpose of chaos theory studies is the various aspects, mainly is to reveal the nature of chaos, portrays its basic characteristics, understood its dynamics condition, and strive to control and use it. Because chaotic system is extremely sensitive to the initial condition which make the system output not meet people's demand, we always need to restrain the chaos in many practical systems. On the other hand, the chaotic system can be beneficial to other systems due to its hard prediction and inner random. Such as, the application of chaos to the secure communications. So it is very important to chaos control and application about how to restrain chaos when it is harmful and how to make use of it when it is useful. And the research on it will have theoretical and real applied value.In this thesis, we draw some results of chaos synchronization through the study of chaos systems, methods of control and synchronization. First some basic notions and definitions about chaos study are systematically introduced, then the main characters of chaos, the way to chaos and the methods of control chaos, the definition of chaos synchronization, the category and the methods of it are introduced, the impulsive differential system definition and some related theorems. Then using inequality analytic method and the method of variation of parameters, discussed a multi-delay chaos systems. In some common chaos systems, its dimensions are finite, and its complexity is not high. It is can easily be deciphered in secure communication. In order to enhance the high-security system randomness and unpredictability, it is necessary to increase the dimension of the system, thus causes the structure of the system to change exceptionally complex. Therefore, we increase the dimension of the system, which obtained a multi-delay the synchronization of chaotic systems. Finally discussed the impulsively synchronized chaotic systems. Using the Lyapunov stable theorem and schur Complement draw on the conclusions of impulsive synchronization of this kind of chaos system...