Research Of Function Projective Synchronization

Currently, the research of the chaotic synchronization problem was widely regarded in each physical academics, such as mechanics, electricity, optical etc., and was also regarded important in many areas as safety communication, long distance communication, chemical reaction, biology network, artificial nerve network, controlling theory etc., especially in the safety communication aspect. By studying and reading the fruit of scholars and experts in researching chaotic synchronization problems, we propose a series of definitions and arithmetic of function projective synchronization, and realized the function projective synchronization of some famous continuous-time chaotic systems and discrete-time chaotic systems. At the same time, we give out the numerical simulations and the analyse of figures.Concerning projective synchronization and function projective synchronization, we do some work as follows:1. Studying the generalized projective synchronization;2. Proposing the function projective synchronization in continuous-time chaotic systems;3. Realizing the function projective synchronization of the discrete-time chaotic systems. The thesis is arranged as follows:Chapter 1 Simply introducing the history development and the present condition of chaos, and the practical meaning of chaotic control and chaotic synchronization.Chapter 2 Introducing the development of projective synchronization since being proposed: projective synchronization, the generalized projective synchronization, the modified projective synchronization, and the function projective synchronization proposed by us.Chapter 3 We researched the function projective synchronization, respectively in continuous-time chaotic systems and discrete-time chaotic systems. And at the end of this chapter, we made some research in chaotic controlling to stabilize the unstable chaotic systems.(1) Proposing the function projective synchronization in two identical continuous-time chaotic systems, and using the active controlling method to realize their function projective synchronization;(2) Realizing the function projective synchronization of two identical hyperchaotic systems;(3) Based on the Lyapunov theory, we propose the function projective synchronization of two different continuous-time chaotic systems and give out the concrete models;(4) In the discrete-time systems, defining and realizing the function projective synchronization; (5) Stabilizing the unsteady chaotic system to its fixed points, and carriying out the steady analyse of two-dimensional Lorenz system and 3D Rossler systems.About the above work, we verified the effect of synchronization and controlling throughout numerical simulations.