Removal, Suppression, and Control of Chaos by Nonlinear Design

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.