The Control And Synchronization Of Chaos System And Analysis To Complex Network System

Chaos is a kind of widespread phenomenon between nature and human society. It appears a kind of irregular and random movement in the certain system, displaying the complexity of things. Recently, chaos control and synchronization have been an active research of the nonlinear subject. This new technology promises to have a significant impact on many novel engineering applications. The challenging research field has become a scientific inter-discipline involving many other fields. In this paper, my dissertation mainly focuses on the chaos control and synchronization and complex networks. And combine together with effective economic system, giving a very valid method to control the economic system. The main content is depicted as follows:1. To the control and synchronization of chaos system in the research background and study conditions are proceeded very full-scale introduction and summaries.2. The usefulness of chaos control for a kind of non-linear chaos finance system is studied. First, the selection of feedback gain matrix and its revision are used to design two kinds of controller to suppress chaos to unstable equilibrium point. Then the Lyapunov direct method and Routh-Hurwith criteria are used to analyze and study the gain's scope of controlled system and the asymptotic stability at the equilibrium point. At last, the validity of the two controlling methods is proved through theoretical analysis and numerical simulations.3. In this paper, we primarily study the problem of chaos control for a new chaotic system. Firstly, it controls the chaotic system to its unstable equilibrium points by designing a speed feedback controller. The Routh-Hurwitz criterion is used to analyze the stability of the controlled system, and the result indicate that the controlled system can converge to nonzero equilibrium points, but it cannot converge to zero equilibrium point. Comparing with the method of state-variable-feedback control shows its superiority. Secondly, we design an approximated delay feedback control method by applying Taylor theorem; it can make the controlled system stabilize the expected periodic orbits or equilibrium points. Finally, the fast-validity of these two kinds of control methods is justified by numericalsimulation.4. Because of many chaotic systems may be regarded as dissipative system. Therefore, there must exist at least one-dimensional stable manifold within the chaotic dynamics. Using these manifolds can design appropriate control strategies. A stable-manifold-based method for realizing the synchronization, namely, when chaotic orbit enters a small neighbor, the controller acts on the nonlinear system. When the trajectories of two unidirectional-coupled chaotic systems arrive at this manifold, the error dynamics is global asymptotical stable at origin. Therefore, it is realizing the synchronization of two chaotic systems. At last, the possibility and effective of this kind of method is tested by analysis and numerical simulating Chen system and Rossler system.5. In this paper, the possibility and development of chaos synchronization in complex networks are introduced in brief. And outlook my work in the future.