Lucubrate On Generalized Synchronization Of Chaotic Systems With Different Structure

The chaos is a kind of irregular complex forms of exercise, widely consist in nature, and other fields. Due to the extreme sensitivity and highly randomness of initial value showed in chaotic motion, it has been affected by the people's extensive concern. As an important research direction, chaos synchronization made significant progress in confidential communications, image processing applications and so on. The generalized synchronization of chaotic systems, especially the different structure of chaotic systems, are more common, general and theoretical. This article mainly studied the generalized synchronization of chaotic systems. Based on the knowledge of matrix and Lyapunov theory of previous scholars, we further discusses the generalized synchronization of chaotic systems with different structures. The main contents of this article are arranged as following:The histories of chaos, research background as well as task arrangement are introduced in the first chapter. In the second chapter, there is some basic theoretical knowledge.In chapter three, we further discuss the generalized synchronization in existence deficiency. Based on the transformation of matrix and Lyapunov stability theory, it is full explored the Jacobin matrix of vector function is reversible or not. Then, we give our theory about generalized synchronization of chaotic systems. At the end of the chapter, we give some simulations with familiar Lorenz system and hyperchaos Chen system, and the simulation proves the correctness of the theory.Using sliding mode method, we talk about generalized synchronization in chapter four. Using the sliding mode control thoughts and choosing appropriate sliding surface, generalized synchronization of different structure is discussed at the condition of sliding mode control. The sliding synchronization method in this chapter expands the theory range and has certain theoretical value.