Automatic control and tracking of periodic orbits in chaotic systems.

Based on an automatic feedback adjustment of an additional parameter of a dynamical system, we propose a strategy for controlling periodic orbits of desired periods in chaotic dynamics and tracking them toward the set of unstable periodic orbits embedded within the original chaotic attractor. The method does not require information on the system to be controlled, nor on any reference states for the targets, and it overcomes some of the difficulties encountered by other techniques. Assessments of the method's effectiveness and robustness are given by means of the application of the technique to the stabilization of unstable periodic orbits in both discrete- and continuous-time systems.