Low-Dimensional Description of Pulses under the Action of Global Feedback Control

Y. Kanevsky; A. A. Nepomnyashchy

Mathematical Modelling of Natural Phenomena (2012)

  • Volume: 7, Issue: 2, page 83-94
  • ISSN: 0973-5348

Abstract

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The influence of a global delayed feedback control which acts on a system governed by a subcritical complex Ginzburg-Landau equation is considered. The method based on a variational principle is applied for the derivation of low-dimensional evolution models. In the framework of those models, one-pulse and two-pulse solutions are found, and their linear stability analysis is carried out. The application of the finite-dimensional model allows to reveal the existence of chaotic oscillatory regimes and regimes with double-period and quadruple-period oscillations. The diagram of regimes resembles those found in the damped-driven nonlinear Schrödinger equation. 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.. "Low-Dimensional Description of Pulses under the Action of Global Feedback Control." Mathematical Modelling of Natural Phenomena 7.2 (2012): 83-94. <http://eudml.org/doc/222236>.

@article{Kanevsky2012,
abstract = {The influence of a global delayed feedback control which acts on a system governed by a subcritical complex Ginzburg-Landau equation is considered. The method based on a variational principle is applied for the derivation of low-dimensional evolution models. In the framework of those models, one-pulse and two-pulse solutions are found, and their linear stability analysis is carried out. The application of the finite-dimensional model allows to reveal the existence of chaotic oscillatory regimes and regimes with double-period and quadruple-period oscillations. The diagram of regimes resembles those found in the damped-driven nonlinear Schrödinger equation. 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 = {Ginzburg-Landau equation; delayed feedback control; finite-dimensional models; solitary waves},
language = {eng},
month = {2},
number = {2},
pages = {83-94},
publisher = {EDP Sciences},
title = {Low-Dimensional Description of Pulses under the Action of Global Feedback Control},
url = {http://eudml.org/doc/222236},
volume = {7},
year = {2012},
}

TY - JOUR
AU - Kanevsky, Y.
AU - Nepomnyashchy, A. A.
TI - Low-Dimensional Description of Pulses under the Action of Global Feedback Control
JO - Mathematical Modelling of Natural Phenomena
DA - 2012/2//
PB - EDP Sciences
VL - 7
IS - 2
SP - 83
EP - 94
AB - The influence of a global delayed feedback control which acts on a system governed by a subcritical complex Ginzburg-Landau equation is considered. The method based on a variational principle is applied for the derivation of low-dimensional evolution models. In the framework of those models, one-pulse and two-pulse solutions are found, and their linear stability analysis is carried out. The application of the finite-dimensional model allows to reveal the existence of chaotic oscillatory regimes and regimes with double-period and quadruple-period oscillations. The diagram of regimes resembles those found in the damped-driven nonlinear Schrödinger equation. The obtained results are compared with the results of direct numerical simulations of the original problem.
LA - eng
KW - Ginzburg-Landau equation; delayed feedback control; finite-dimensional models; solitary waves
UR - http://eudml.org/doc/222236
ER -

References

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