Chaos Control And Synchronization Of Extended Duffing-van Der Pol System

At present, the theory of chaos control and synchronization is a hot topic in the international research field. Especially, the successful application of chaos synchronization in the field of secure communication and laser control has opened up a broad practical prospect to the theoretical research of chaos. It is known that the famous Duffing-Van der Pol system has broad practical background. In this dissertation, the problem of chaos control and chaos synchronization of the real extended Duffing-Van der Pol system and the problem of chaos control of the complex system are investigated. This dissertation is divided into five chapters. The concrete contents of the dissertation are as follows:In the first chapter, the history and the research survey are reviewed. Then, the concept of chaos, some methods and tools in common use and the elementary knowledge used in this dissertation are introduced briefly. At last, the writing arrangements are given.In the second chapter, for the extended Duffing-Van der Pol system with double potential well, the problem of dynamic behavior and chaos control is investigated under the non-symmetry biharmonical excitation. According to the analysis about the joint control diagram of phase versus amplitude about the additive non-symmetry harmonical excitation and the numerical results, the random phase parallel movement method is put forward for the first time to suppress the chaos in this system. Then, the mechanism and the robustness about the chaotic behavior that can be controlled with the random phase are discussed from the view of probability and statistics. The numerical results and simulations show the validity of this method and the correctness of the conclusion.In the third chapter, the problem of the chaos control of the complex extended Duffing-Van der Pol system is investigated. The results show that the solution of the complex system with specific parameters has chaotic behavior. The random phase with proper noise intensity can suppress the chaotic trajectory in the phase space onto a limit-cycle with certain width. The analysis to the joint control diagram shows the very weak non-symmetry biharmonical excitation can effectively suppress the chaotic behavior of the system. The simulations show that this method is better than the...