Chaos System's Lyapunov Exponents And Synchronization

Chaos system's Lyapunov exponents and synchronization are one of the most hot spots in the field of non-linear scientific. So this paper is mainly discussed the algorithm of Lyapunov exponents and synchronization of chaotic system with different structure,and we mainly do the research as follows:First of all, the paper represents the development and the current status of the research on synchronization of chaos and Lyapunov exponents, introduces the several judgment method of chaos.Secondly, introduces the mathematical basis on the Lyapunov exponents, the algorithm of Lyapunov exponents,and Lyapunov exponents's characters. Expounds the wide application of Lyapunov exponents. And calculate Lyapunov exponents of simple mapping.Thirdly, based on software in Matlab, through applied method of 4-order Runge-kutta and G-S orthogonal program,the algorithm of Lyapunov exponents is designed. And calculated some chaos system's Lyapunov exponents.Therefore,this program has accuracy,efficiency and suitability.Finally, introduces the method of active synchronization and adaptive synchronization of system, based on these methods and Lyapunov stability theory, achieved synchronization of two chaotic different systems with unknown parameters between Lorenz system and Rossler system,and the same time, achieved synchronization of different systems with unknown parameters between hyperchaotic Lorenz system and hyperchaotic Rossler system.And numerical simulations show the effectiveness and feasibility of these methods.