STABILIZING AND TRACKING UNSTABLE FOCUS POINTS IN CHAOTIC SYSTEMS USING A NEURAL-NETWORK

We present a control system containing a neural network for stabilizin g chaotic orbits on an unstable focus point embedded within a chaotic attractor. This control system does not require the location of the un stable focus point and the local linearized dynamics at the point. Eve n if a parameter of the chaotic system changes slowly, the control sys tem can automatically track the unstable focus point both within and o utside the chaotic regimes. We test the control system using a nonline ar map in numerical experiments.