Open-loop sustained chaos and control: A manifold approach

Year: 2002

Authors: Schwartz I.B., Triandaf I., Meucci R., Carr T.W.

Autors Affiliation: Nonlinear System Dynamics Section, U.S. Naval Research Laboratory, Plasma Physics Division, Code 6792, Washington, DC, 20375-5000, United States; Istituto Nazionale di Ottica Applicata, Florence, 50125, Italy; Department of Mathematics, Southern Methodist University, Dallas, YX, 75275-0156, United States

Abstract: We present a general method for preserving chaos in nonchaotic parameter regimes as well as preserving periodic behavior in chaotic regimes using a multifrequency phase control. The systems considered are nonlinear systems driven at a base frequency. Multifrequency phase control is defined as the addition of small subharmonic amplitude modulation coupled with a phase shift. By implementing multifrequency control, stable and unstable manifold intersections in postcrisis regimes may be manipulated to sustain chaos as well as to sustain periodic behavior. The theory and a preliminary experiment are demonstrated for a CO2 driven laser.

Journal/Review: PHYSICAL REVIEW E

Volume: 66 (2)      Pages from: 026213-1  to: 026213-7

KeyWords: Chaos systems; Design parameters; Phase space; Population models, Amplitude modulation; Bifurcation (mathematics); Boundary conditions; Frequencies; Nonlinear systems; Phase control; Phase shift; Statistical mechanics, Chaos theory
DOI: 10.1103/PhysRevE.66.026213

Citations: 15
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