Projective Synchronization Of Time-delayed Chaotic Systems

Chaos is a kind of irregular movement occurred in the deterministic system. Chaotic synchronization usually refers to a coherent phenomena between two or more vibration system. In the last few years, chaos synchronization has been a theme in nonlinear science and gained a lot of attention for its potentials applications in some engineering application, such as image processing, chemical and biological systems, information science and in particular secure communication. In this paper, modified function projective synchronization scheme between chaotic and time-delayed chaotic systems with parameters is proposed.Based on the adaptive synchronization method and combined with the Lyapunov stability theory, discussed modified function projective synchronization between several classic chaotic system and time-delayed chaotic system. This paper is divided into three chapters, the main contents are as follows:The first chapter describes the origin and development of chaos,the definition of chaos and chaos synchronization, and several classification and implementation method of chaos synchronization.In this last, introduces the main contents of this paper.In the second chapter, based on Lyapunov stability theory, adaptive controllers and parameter updating laws are designed to achieve the function projective synchronization between chaotic and time-delayed chaotic system. The scheme is applied to realize the synchronization between time-delayed Lorenz systems and time-delayed hyper-chaotic Chen systems, respectively. Numerical simulations are also presented to show the effectiveness of proposed method.In the third chapter, use the method similar as the third chapter achieve the projective lag synchronization.The scheme is applied to realize the synchronization between time-delayed Lorenz system and time-delayed Rossler system, numerical simulations are also presented to show the effectiveness of proposed method.In the last, the research work of this paper is summarized and the possible is further proposed.