Controlling unstable periodic orbits in a nonlinear optical system: the Ikeda map

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Title: Controlling unstable periodic orbits in a nonlinear optical system: the Ikeda map
Author: Alsing, Paul; Gavrielides, Athanasios; Kovanis, Vassilios
Abstract: With the publication of the seminal paper by Ott, Grebogi and Yorke (OGY) [l] the concept of controlling chaos has become part of the lexicon of physicists and engineers dealing with chaotic nonlinear dynamical systems. The authors showed that by using small, judiciously applied perturbations the unstable periodic orbits, which are dense in a chaotic attractor, could be stabilized. The strength of their approach lies in the absence of the necessity for any a priori analytical model of the chaotic system in order to affect the control. The information required to construct the controlling perturbations can be extracted from experimental time series obtained from the unperturbed system. Since the publication of [l], the OGY controlling algorithm, and numerous variations upon its central concepts, have been implemented numerically and experimentally in a host of nonlinear dynamical systems ranging from lasers and electronic circuits to chemical and biological systems. For excellent review articles see [2] and the references therein.
Description: ©1994 Institute of Electrical and Electronics Engineers (IEEE). Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.
Record URI: http://hdl.handle.net/1850/4702
Date: 1994-07-25

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