Preserving Transients on Unstable Chaotic Attractors

Abstract

In this chapter we present a controlling method which allows the preservation of transient chaotic evolution in the desired region of the phase space. The concept of practical stability for the perturbed chaotic attractors and the connection between practical and asymptotic stability is described. Our controlling procedure allows asymptotically unstable chaotic attractors to become practically stable in such a way that transients on the unstable chaotic attractors or in their neighborhoods do not decay. Illustrative applications are presented.