| Since Chaos have been found, many scholars continually study and explore the mechanism of this phenomenon. Many new chaotic systems and new chaos attractor have been found. And then, before 1990 the Chaos control had proved to be practicable, the study of the chaos control quickly become the hottest area of the chaos reseach. From then on, people began to study the application of chaos.This article's first two chapters introduced the origin and development of chaos and basic knowlidge of nonlinear dynamics, including the definition and property of chaos, chaos eigenvector, chaos control and synchronization and mainly methods of controls.In the next three chapters, the third chapter studied the basic properties of Rossler 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 and the fifth chapters, we studied on the control of Rossler system. On the facet of chaos control, we proposed two methods by which controls the Rossler system to a balanced point by using linear feedback, and make the improve and value emulate. On the facte of chaos synchronization, by the nonlinear function feedback control, designed one controller to control two systems which have different initiation to achieve to synchronization. Improve the controller by the Lyapunov function method shows the availability of it. And the value emulate of the controller shows the validity of it. Finally, the sixth chapter summarized the work of the paper and prospected the future of chaos studies.
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