Research On The Synchronization Problems Of A Class Of Chaotic Systems

As a phenomenon found in nonlinear dynamic system, chaos is deterministic and random-like. It exists in the world everywhere. And it has been intensively applied in various fields such as biology, physics, chemistry, engineering and information. Base on the sensitive dependence of chaotic systems on their initial conditions, a large number of non-periodic, continuous broadband frequency spectrum, noise-like, but deterministic and reproducible signals can be generated, therefore particularly suitable for secure communication and other areas. Chaos synchronization has become the key technique in secure communications, which has achieved rapid development, and there have lots of remarkable results reported about it since1990s.The synchronization of a class of identical and different structures chaotic systems in-depth study in this thesis. The main contributions are listed as follows:Chaos synchronization of a class of chaotic systems with the same structure are studied. Firstly, the coupled synchronization of three Lorenz chaotic systems is achieved using the principal minor sequence method. Secondly, the active control method realized the global synchronization of three Lu systems, and active controller is designed at the same time. Finally, through the thought by active control, we propose a new method of variable feedback synchronization of three identical chaotic systems, according to which judgment of coupling parameter and design of active the controller are done. The results of numerical simulation with Matlab illustrate the effectiveness of the proposed method.According to a class of different chaotic systems, and also based on Lyapunov stability theorem, we propose an improved response-drive-response synchronization method of different structures of three chaotic systems, designing out effective controller, realizing the synchronous among New system, Lorenz system and Rossler system. Then through the thought by active control, we propose a new method of variable feedback synchronization of three different structures chaotic systems, according to which judgment of coupling parameter and design of active the controller are done, thus fulfills the Chen system, Lu system and Lorenz system feedback synchronization. The results of numerical simulation with Matlab illustrate the effectiveness of the proposed method.Lastly, the summary of the whole dissertation is given and the research directions in future are put forward.