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Patterns and Waves Generated by a Subcritical Instability inSystems with a Conservation Law under the Action of a Global FeedbackControl

Published online by Cambridge University Press:  09 June 2010

Y. Kanevsky  and
A.A. Nepomnyashchy
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Abstract

A global feedback control of a system that exhibits a subcritical monotonic instabilityat a non-zero wavenumber (short-wave, or Turing instability) in the presence of a zeromode is investigated using a Ginzburg-Landau equation coupled to an equation for the zeromode. The method based on a variational principle is applied for the derivation of alow-dimensional evolution model. In the framework of this model the investigation of thesystem’s dynamics and the linear and nonlinear stability analysis are carried out. Theobtained results are compared with the results of direct numerical simulations of theoriginal problem.

Keywords

feedback controlpattern formationvariational approach

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