基于稳定流形的方法实现混沌系统的同步

Stable-manifold-based method for realizing chaos synchronization

在非保守自治系统中,许多混沌系统都可作为耗散系统,因此,在这样的混沌系统中存在至少一维的稳定流形,利用这些流形可以设计恰当的控制策略.基于稳定流形的方法实现混沌系统的同步是当混沌轨道进入到稳定流形的小邻域内的时候,开始施加控制信号.一旦两个非直接耦合的混沌系统的轨迹到达这些稳定流形,其误差系统渐进趋于原点,从而实现两系统的同步.并通过Chen系统和Rossler系统的分析和数值模拟研究验证了这种方法的可行性与有效性.

Many chaotic systems can be regarded as dissipative systems. So, there must exist at least one-dimensional stable manifold within the chaotic dynamics. By using these manifolds we can design appropriate control strategies. A stable-manifold-based method for realizing the synchronization is, namely, when chaotic orbit enters a small neighbor, the controller acts on the nonlinear system; when the trajectories of two unidirectional-coupled chaotic system arrive at this manifold, the error dynamics is global asymptotical stable at origin. Therefore, the synchronization of two chaotic systems is realized. Finally, the possibility and effectiveness of this method are tested by numerical simulations on Chen system and Rossler system.