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

Y. Kanevsky; A.A. Nepomnyashchy

Mathematical Modelling of Natural Phenomena (2010)

  • Volume: 6, Issue: 1, page 188-208
  • ISSN: 0973-5348

Abstract

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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.

How to cite

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Kanevsky, Y., and Nepomnyashchy, A.A.. "Patterns and Waves Generated by a Subcritical Instability in Systems with a Conservation Law under the Action of a Global Feedback Control." Mathematical Modelling of Natural Phenomena 6.1 (2010): 188-208. <http://eudml.org/doc/197620>.

@article{Kanevsky2010,
abstract = {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.},
author = {Kanevsky, Y., Nepomnyashchy, A.A.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {feedback control; pattern formation; variational approach; Turing instability; low-dimensional evolution model; linear stability analysis; nonlinear stability analysis},
language = {eng},
month = {6},
number = {1},
pages = {188-208},
publisher = {EDP Sciences},
title = {Patterns and Waves Generated by a Subcritical Instability in Systems with a Conservation Law under the Action of a Global Feedback Control},
url = {http://eudml.org/doc/197620},
volume = {6},
year = {2010},
}

TY - JOUR
AU - Kanevsky, Y.
AU - Nepomnyashchy, A.A.
TI - Patterns and Waves Generated by a Subcritical Instability in Systems with a Conservation Law under the Action of a Global Feedback Control
JO - Mathematical Modelling of Natural Phenomena
DA - 2010/6//
PB - EDP Sciences
VL - 6
IS - 1
SP - 188
EP - 208
AB - 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.
LA - eng
KW - feedback control; pattern formation; variational approach; Turing instability; low-dimensional evolution model; linear stability analysis; nonlinear stability analysis
UR - http://eudml.org/doc/197620
ER -

References

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