A map-based algorithm for controlling low-dimensional chaos

A simple proportional-feedback algorithm for controlling chaos is presented. The scheme is a map-based variation of a method recently proposed by Ott, Grebogi, and Yorke [Phys. Rev. Lett. 64, 1196 (1990)] in which unstable periodic orbits embedded within a strange attractor are stabilized through de...

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Bibliographic Details
Published inThe Journal of chemical physics Vol. 96; no. 10; pp. 7506 - 7513
Main Authors Petrov, Valery, Peng, Bo, Showalter, Kenneth
Format Journal Article
LanguageEnglish
Published Woodbury, NY American Institute of Physics 15.05.1992
Subjects
Chemistry
Exact sciences and technology
General and physical chemistry
General. Nomenclature, chemical documentation, computer chemistry
Theory of reactions, general kinetics. Catalysis. Nomenclature, chemical documentation, computer chemistry
Chaos
Theoretical study
Algorithm
Chemical system
Chemical model
Biological model
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ISSN0021-9606
1089-7690
DOI10.1063/1.462402

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Summary:A simple proportional-feedback algorithm for controlling chaos is presented. The scheme is a map-based variation of a method recently proposed by Ott, Grebogi, and Yorke [Phys. Rev. Lett. 64, 1196 (1990)] in which unstable periodic orbits embedded within a strange attractor are stabilized through deliberate perturbations of a system constraint. The simplified method offers advantages for control of systems in which more complicated algorithms might not be feasible due to short time scales or limited computational resources. Applications to chemical and biological models are presented to demonstrate the utility and limitations of the method. Low-dimensional chaos can usually be stabilized through proportional feedback of one parameter; in some cases, however, a linear combination of several parameters must be utilized.
ISSN:0021-9606
1089-7690
DOI:10.1063/1.462402