# 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

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topKanevsky, 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 -

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