Synchronization Study Of Four-wing Chaotic Systems

Chaos Theory as a fundamental part of nonlinear science is an important branch of nonlinear science. Because of its broad application prospects in chaotic secure communication and many engineering fields, in recent years, many researchers pay much attention to it. Chaos synchronization technology as the basis for secure communication systems, many scientists devoted a lot of time and effort. Over the years, researchers have proposed to learn a variety of chaotic synchronization method. For example, Complete synchronization, generalized synchronization. These methods can be effective to achieve synchronization. In the vigorous development of chaos synchronization technology at the same time, chaos control technology has made considerable progress.In many engineering fields, it need to control chaos effectively. For example, to eliminate the original chaotic system; or the original chaotic system track stabilization to a certain track. This article call two modes of operation of the original chaotic system as Chaos Control. This article focuses on the chaos synchronization of hyperchaotic systems and a comprehensive analysis of various types of synchronization implementation, mathematical proof and numerical simulation confirmed its effectiveness. The main work are as follows:(1) First of all,this article discuss several methods of chaotic synchronization, and then discussed the multi-switch synchronization of Lorenz and Chen-Lee system based on the adaptive control method. And this article talk about the chaotic controller and parameter identification rules on the state of each switch value respectively. Based on Lyapunov stability theory, this article design the chaos controller parameter identification rules,and with its help, the drive and response systems achieve the synchronization. Numerical simulation have come to the same conclusion.(2) This article research the four-dimensional chaotic system synchronization problems in the parameters are known and unknown parameters for a class of real four-wing chaotic system synchronization scheme.In unknown parameters case, this article use the same structure method.And in parameters known case, this article use different structure method. Based on Lyapunov stability theory, the chaotic controller and the corresponding parameter update rules achieve the complete synchronization of drive and response system.In the case of unknown parameters, with the help of parameter identification rules, the unknown parameters is identified out. The theoretical proof and numerical simulations have confirmed the effectiveness of the method. (3) After complete synchronization, this article continue to discuss the four-wing chaotic system anti-synchronization scheme. The parameters are known and unknown parameters cases combined with the same structure and different structures. Our chaotic controller and the corresponding parameter update rules achieve the anti-synchronization of drive and response system.In the case of unknown parameters, with the help of parameter identification rules, the unknown parameters is identified out. The theoretical proof and numerical simulations have confirmed the effectiveness of the method.(4) With the depth of the problem, without loss of generality, this article study a four-dimensional chaotic system function projective synchronization problem with extending the definition of error a lot.And the next chapter, this article continue to expand the definition of the error. The ratio function is defined as function of the time variable t. At this time, this article call chaos synchronization as the modified function projective synchronization. Then this article give the most generalized synchronous controller.Drive and response systems achieve the modified function projective synchronization with its help.