Dynamics Analysis Of Chaos Circuit And Chaotic Control

Chaos is a random state appeared in the nonlinear systems, which does not need any additional quasi-random behavior. Chaotic system possesses mixing characteristics of local instability and global stability. Besides, it is sensitive dependent on initial conditions. If the initial conditions are changed small, the system will present exponential growth with time evolution.This thesis mainly includes three aspects as follows.Firstly, the development of chaos, the problems of nonlinear dynamics on chaotic circuit, and the applications of insecure communications are introduced. The basic theories, the essence features and the identification methods of chaos are gived.Secondly, according to jacobian matrix method, the dynamics for a class of Chua’s dual chaotic circuit is analyzed in detail. The problems, such as the basic properties, the equilibrium points, and the stability etc, are discussed. The result that the system is influenced by the system parameters is presented. The numerical simulations are used to verify the theoretical results, and to show the existence of various states of the system with various parameters.Finally, according to the specific structure of Liu chaotic system and the stability theory of differential equation, the proportional-differential feedback control method is applied to control Liu system. The third state variable is chosen as the driving variable and effective controller is designed. So, the problem on the stabilization of three unstable equilibrium points for Liu chaotic system is solved. Furthermore, these points are asymptotically stable. Meanwhile, by the numerical simulation we find that control results will be affected by the different values of adjustable parameters in the controller. The simulation results show the method of proportional-differential feedback control is simple, efficient and easy to achieve. It has a great value to be applied in actual engineering.