Synchronization for hyperchaotic Chen system and hyperchaotic R?ssler system with different structure

Abstract

In this paper two different methods——active control synchronization method and adaptive synchronization method are presented to study hyperchaotic Chen system and hyperchaotic Rssler system with different structure. Two different controllers are designed for synchronizing response system and drive system. When the parameters are known in advance, active control synchronization is adopted, the method is simple without constructing Lyapunov function and the time which realizes synchronization is short, when the parameters are fully unknown, the analytical expression of synchronization controller and adaptive law of parameters is given based on Lyapunov stability theory, which makes the different systems reach to synchronization and identifies the unknown parameters. Numerical simulation shows the effectiveness and feasibility of these two methods.