Patterns and Waves Generated by a Subcritical Instability in Systems with a Conservation Law under the Action of a Global Feedback Control

A global feedback control of a system that exhibits a subcritical monotonic instability at a non-zero wavenumber (short-wave, or Turing instability) in the presence of a zero mode is investigated using a Ginzburg-Landau equation coupled to an equation for the zero mode. The method based on a variati...

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Bibliographic Details
Published in:Mathematical modelling of natural phenomena 2011, Vol.6 (1), p.188-208
Main Authors: Kanevsky, Y., Nepomnyashchy, A.A.
Format: Article
Language:English
Subjects:
35B36
93B52
feedback control
Feedback control systems
Mathematical models
Numerical analysis
pattern formation
Simulation
variational approach
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Summary:A global feedback control of a system that exhibits a subcritical monotonic instability at a non-zero wavenumber (short-wave, or Turing instability) in the presence of a zero mode is investigated using a Ginzburg-Landau equation coupled to an equation for the zero mode. The method based on a variational principle is applied for the derivation of a low-dimensional evolution model. In the framework of this model the investigation of the system’s dynamics and the linear and nonlinear stability analysis are carried out. The obtained results are compared with the results of direct numerical simulations of the original problem.
ISSN:0973-5348
1760-6101
DOI:10.1051/mmnp/20116110