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REVIEW ARTICLES

Removal, Suppression, and Control of Chaos by Nonlinear Design

[+] Author and Article Information
John F. Lindner, William L. Ditto

Applied Chaos Laboratory, School of Physics, Georgia Institute of Technology, Atlanta GA 30332

Appl. Mech. Rev 48(12), 795-808 (Dec 01, 1995) (14 pages) doi:10.1115/1.3005094 History: Online April 29, 2009

Abstract

Techniques to remove, suppress, and control the chaotic behavior of nonlinear systems are reviewed. Analysis of a forced damped nonlinear oscillator provides a brief overview of the relevant nonlinear dynamics of dissipative systems. Various techniques for suppression and control of chaos are then outlined, compared and contrasted. A unified mathematical notation facilitates the comparison. The successes of each strategy in numerical simulations and physical experiments are carefully noted. Their strengths and weaknesses are analyzed, and they are evaluated according to whether they employ feedback, are goal-oriented, are model-based, merely remove chaos–or truly exploit it. An elementary derivation of the important OGY control equation is supplied. Critical references provide an entry into the literature. It is argued that nonlinearity can be a real-world advantage, and it is hoped that this review will serve as summary of, and invitation to, the nascent field of nonlinear design.

Copyright © 1995 by The American Society of Mechanical Engineers
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