A Discontinuous Parameter-Perturbation Method to Control Chaotic Systems

A new method is introduced for controlling chaos in continuous systems, and stabilizing one of the unstable periodic orbits embedded in the chaotic attractor. The stabilization of the orbit is obtained by applying a discontinuous perturbation to one parameter of the system in a neighborhood of the orbit. The analysis is carried out by means of Poincare surfaces, which makes possible to develop the method based on previous results applicable to discrete systems. The discrete nature of the method allows to stabilize three-dimensional systems applying only two changes to the parameter, although in principle more changes may be applied for each period of the orbit. The method is easily generalized to n-dimensional continuous systems of higher order.