Anti-synchronization And Dual Synchronization Research Of A Novel Chaotic System

Nonlinear science is a discipline of nonlinear fields. Particularly, Chaos theory is one of important subdiscipline of nonlinear science. It is not only widespread in nature, but in social life.This paper investigates a novel three-dimensional autonomous chaotic system on the basis of the existing chaos system. the system is researched some dynamic characteristics by theoretical analysis and computer simulations. In addition, this article also studies from the structure and different dimension of different structure of synchronization, as well as its dual synchronization issues because the chaotic system is widely used in all walks of life. The main contents of this paper are as follows:The first chapter is the introduction. The related chaos theories are introduced which include the generation and development of chaos theory, the definition of chaos and some chaos systems used in the following article. Finally, this article respectively introduces the anti-synchronization of chaotic systems and dual synchronization of chaotic systems. The second chapter is stability theory. The principles of Lyapunov stability are introduced which include method of Lyapunov function and direct discriminant method. The third chapter proposes a new three-dimensional autonomous chaotic system on the basis of the existing chaos system. Some basic dynamical properties of the new system are analyzed by means of theoretical analysis and computer simulations, such as dissipation of the system, the existence of attractor, the stability of the equilibria, Lyapunov exponents, Lyapunov dimension, the sensitivity of initial value and power spectrum. The results show that the chaotic system has abundant dynamical behavior. The fourth chapter mainly studies the anti-synchronization of chaotic systems. On the one hand, anti-synchronization of the new chaotic system is achieved by the design of nonlinear controller. On the other hand, designing of nonlinear controller by add-dimension method make Lorenz system and a new chaotic system achieve anti-synchronization. They are proved by direct criterion theory in the Laplace transform method which is different from the previous v function criterion based on Lyapunov stability theory. Eventually, it validates the above theoretic results in numerical simulations. The fifth chapter mainly studies dual synchronization of chaotic systems. Firstly, the related dual synchronization theories are studied and the design of gain vector controller makes chaos systems achieve dual synchronization. Secondly, we use the dual synchronization of the new chaotic system and Chen chaotic system as an example to prove the rationality andfeasibility of the above theories by the theoretic analysis and numerical simulation. Finally, to further validate the effectiveness of this method, giving an example of the different dimensions of new chaotic system and hyper chaotic Lorenz system of dual synchronization to prove the rationality and feasibility of the above theories. The results show that above methods are correct.