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, or stationary) behavior. We review the major ideas involved in the control of chaos, and present in detail two methods: the Ott-Grebogi-Yorke (OGY) method and the adaptive method. We also discuss a series of relevant issues connected with chaos control, such as the targeting problem, i.e., how to bring a trajectory to a small neighborhood of a desired location in the chaotic 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 discuss the issues of communicating with chaos by controlling symbolic sequences and of synchronizing chaotic systems. Finally, we give a review of relevant experimental applications of these ideas and techniques.
an advanced textbook on the theory of deterministic, stochastic and quantum chaotic / turbulent systems
Geometry of chaos - any scientist, engineer or mathematician would profit from understanding nonlinear dynamics on this level.
Chaos rules - a challenge for a seasoned theorist
Chaos and Fractals - New Frontiers of Science
Chaos Theory and Its Implications for Social Science Research
Science of Chaos or Chaos in Science?
Chaos Bound: Orderly Disorder in Contemporary Literature and Science
Chaos, Clio, and Scientific Illusions of Understanding