Studies Of Control And Synchronization Of Chaos And Hyperchaos

Chaos is a kind of special type in the nonlinear dynamical system, it widely lies in nature. Recently, chaos control and synchronization have been an active research of the nonlinear subject. This new technology promises to have significant impact on many novel engineering applications. The challenging research field has become a scientific inter-discipline involving many other fields. The thesis mainly focuses on the control of chaos and synchronization of hyperchaos of nonlinear system. The main content is depicted as follows:Firstly, in first two chapters, control and synchronization of chaos and hyperchaos in the research background and study conditions are introduced, the basic theory of chaos dynamics is presented.In the third chapter, we primarily study the problem of adaptive control for Liu chaotic system. The local dynamical behavior of the Liu system is discussed with complementary-cluster energy-barrier criterion (CCEBC). Then, adaptive controllers are designed and the analytical expression of controllers and adaptive law of unknown parameters are given based on Lyapunov stability theory. With this method, parameters identification and chaos control can be achieved simultaneously with one and two controllers. The Matlab software is used to prove the effectiveness of this method.The forth chapter discusses coupled synchronization of hyperchaotic system. A new approach for realizing the synchronization of two linearly coupled hyperchaotic systems is applied. This method is based on the theory of stability of linear time-varying systems: it realizes the synchronization by transferring high time-varying systems into low linear constant coefficient system. The new hyperchaotic Chen system and hyperchaotic Rossler system are treated as numerical examples.In the fifth chapter, we discuss the synchronization of two different hyperchaotic systems. Twodifferent methods-active control synchronization method and adaptive synchronization methodare presented to study hyperchaotic Chen system and hyperchaotic Rossler system with different structure. Different controllers are designed for synchronizing response system and drive system.