Control And Synchronization For A Chaotic And A Hyperchaotic System

Chaotic dynamics is a new subject, chaotic is unstable itself, it is sensitive to the initial value. A chaotic attractor is ensured by two things, one is that the system has a trapping region which guarantees the existence of an attractor, the other is that the system displays chaotic behavior on the attractor. The thesis mainly focuses on the control and synchronization of chaos of nonlinear system. The main content is depicted as follows:In chapter 1, background and study conditions of chaos are introduced.In chapter 2, the basic theory and the definition of the control and synchronization for chaos dynamics are presented.In chapter 3, we consider the issues of chaotic control and chaotic synchronization for a new presented chaotic system. In the chaotic control, when the parameter is known, two linear controllers are designed and a sufficient condition is presented to stabilize the chaotic system to any unstable equilibrium points, control the pre-image and control over their images are compared to more graphically illustrate the control of an effective and scientific. Meanwhile, In the chaotic synchronization, two different issues of chaotic synchronization are designed: 1. when the parameter is known, two nonlinear controllers are designed and a sufficient condition is presented to assure globally complete synchronization; 2. when the parameter is unknown, three nonlinear controllers are designed, an adaptive role for estimating the unknown parameter is found and a sufficient condition is presented to assure globally complete synchronization. Theoretical analysis and numerical simulation show that the design is feasible.In chapter 4, we consider the issues of hyper-chaotic control and hyper-chaotic synchronization for a new presented hyper-chaotic system: In the hyper-chaotic control , when the parameter is known, two controls are designed scientifically, One is linear controller, the other is velocity feedback controller, and sufficient conditions are presented to stabilize the chaotic system to any appointed unstable equilibrium points, control the pre-image and control over their images are compared to more graphically illustrate the control of an effective and scientific. In the hyper-chaotic synchronization, when the parameter is unknown, four nonlinear controllers and an adaptive role for estimating the unknown parameter are designed scientifically, and a sufficient condition is presented to assure globally complete synchronization. Theoretical analysis and numerical simulation show that the design is feasible.In chapter 5, we give the summary of the work and the prospect of research and application of chaos.