Some Studies Of Chen's Chaos System

This article's first two chapters introduced the origin and development of chaos and basic knowledge of nonlinear dynamics, including the definition and property of chaos, chaos eigenvector, chaos control and synchronization and mainly methods of controls.In the next two chapters, the third chapter studied the basic properties of Chen's system, stable state and Lyapunov exponential. Analyzed the stability of stable state and proposed two kinds of method to solve the Lyapunov exponential and compared the two results.In the fourth chapter, we studied on the control of Chen's system. On the facet of chaos control ,we proposed three methods by which controls the Chen's system to a balanced point by using linear feedback and one method that using nonlinear feedback control the system to cycle orbit, and make the improve and value emulate. On the facet of chaos synchronization, by the principium of drive-respond, designed four kinds of nonlinear feedback controller to control two systems which have different initiation to achieve to synchronization. Improve one of the controllers by introducing a lemma and the Simulation shows the availability of it. And then use the coupling synchronization control method and self-adapting synchronization control method separately to study the known and unknown drive parameter. Obtain the ideal control methods.Finally, the fifth chapter summarized the work of the paper and prospected the future of chaos control.