# 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

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topKanevsky, 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 -

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