Controlling chaos to generate aperiodic orbits

Abstract

We show how a chaotic system is able to generate a desired aperiodic orbit by making only small temporal perturbations to an available set of system parameters. The appropriate controls are obtained by applying the method developed by Ott, Grebogi, and Yorke [Phys. Rev. Lett. 64, 1196 (1990)] to an artificially constructed dynamical system such that when this dynamical system is at its steady state the output of the chaotic system should be the desired aperiodic orbit. We illustrate our method with some numerical examples in which the motion of a chaotic system is converted to two different aperiodic orbits.