A stable-manifold-based method for chaos control and synchronization

A stable-manifold-based method is proposed for chaos control and synchronization. The novelty of this new and effective method lies in that, once the suitable stable manifold according to the desired dynamic properties is constructed, the goal of control is only to force the system state to lie on the selected stable manifold because once the stable manifold is reached, the chaotic system will be guided towards the desired target. The effectiveness of the approach and idea is tested by stabilizing the Newton–Leipnik chaotic system which possesses more than one strange attractor and by synchronizing the unified chaotic system which unifies both the Lorenz system and the Chen system.