Entrainment and migration control of chaotic systems

Abstract

In this chapter, the entrainment and the migration methods of chaos control are discussed. The background of entrainment and migration control is based on two facts: a multi-attractor chaotic system is sensible to both initial values and parameters and each stable attractor has its basin of attraction. A common goal of chaos control is to steer the trajectory of a chaotic system to a periodic orbit which itself is a solution of the chaotic system. Sometimes, one wants to steer the trajectory to a predesigned orbit which is not the solution of the chaotic system. For some multiple attractor chaotic systems, one would like to direct the trajectory from one attractor to the others. To achieve these goals, entrainment and migration methods are developed. We first introduce these methods and their extension, the open-plusclosed-loop (OPCL) method. Based on the OPCL method, a new control scheme, the open-plus-nonlinear-closed-loop (OPNCL) method, is developed. In addition, we apply the method of OPNCL to a class of dynamical systems, both continuous time and discrete time.