The control of chaos: Theory and applications

S. Boccaletti, C. Grebogi, Ying-Cheng Lai, H. Mancini, D. Maza

Research output: Contribution to journalReview article

672 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)103-197
Number of pages95
JournalPhysics Report
Volume329
Issue number3
DOIs
StatePublished - May 2000

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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    Boccaletti, S., Grebogi, C., Lai, Y-C., Mancini, H., & Maza, D. (2000). The control of chaos: Theory and applications. Physics Report, 329(3), 103-197. https://doi.org/10.1016/S0370-1573(99)00096-4