The control of chaos: theory and applications

Control of chaos refers to a process wherein a tiny perturbation is applied to a chaotic system, in order to realize a desirable (chaotic, periodic, o r stationary) behavior. We review the major ideas involved in the control o f chaos, and present in detail two methods: the Ott-Grebogi-Yorke (OGY) met hod and the adaptive method. We also discuss a series of relevant issues co nnected with chaos control, such as the targeting problem, i.e., how to bri ng a trajectory to a small neighborhood of a desired location in the chaoti c attractor in both low and high dimensions, and point out applications for controlling fractal basin boundaries. In short, we describe procedures for stabilizing desired chaotic orbits embedded in a chaotic attractor and dis cuss the issues of communicating with chaos by controlling symbolic sequenc es and of synchronizing chaotic systems. Finally, we give a review of relev ant experimental applications of these ideas and techniques. (C) 2000 Elsev ier Science B.V. All rights reserved.