Stability of localized solutions in a subcritically unstable pattern-forming system under a global delayed control

B. Y. Rubinstein, A. A. Nepomnyashchy, and A. A. Golovin

Phys. Rev. E 75, 046213 – Published 25 April 2007

Abstract

The formation of spatially localized patterns in a system with subcritical instability under feedback control with delay is investigated within the framework of globally controlled Ginzburg-Landau equation. It is shown that feedback control can stabilize spatially localized solutions. With the increase of delay, these solutions undergo oscillatory instability that, for large enough control strength, results in the formation of localized oscillating pulses. With further increase of the delay the solution blows up.

Received 28 September 2006

DOI:https://doi.org/10.1103/PhysRevE.75.046213

Authors & Affiliations

B. Y. Rubinstein¹, A. A. Nepomnyashchy², and A. A. Golovin³

¹Department of Mathematics, University of California, Davis, California 95616, USA
²Department of Mathematics and Minerva Center for Nonlinear Physics of Complex Systems,Technion—Israel Institute of Technology, Haifa 32000, Israel
³Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, Illinois 60208-3100, USA

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Issue

Vol. 75, Iss. 4 — April 2007

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covering statistical, nonlinear, biological, and soft matter physics