Driving Trajectories in Chaotic Systems

This work presents the main ideas and the fundamental procedures for guiding trajectories on chaotic systems and for stabilizing chaotic orbits, all with the use of small perturbations. We consider an extension of the Ott-Grebogi-Yorke method of controlling chaos and an associated procedure for guiding trajectories on chaotic sets of high dimensional systems. We argue that those techniques can be used even if the chaotic invariant set is nonattractive. As nonattractive chaotic invariant sets commonly exist embedded in high dimensional systems, we also argue that we can combine chaotic control techniques with system control strategies to generate a powerful mechanism for manipulating the dynamics. We present an example in which we change and alter system's evolution at will using only small perturbations to some accessible parameter.