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Shklyaev, Sergey
and
Nepomnyashchy, Alexander
2017.
Longwave Instabilities and Patterns in Fluids.
p.
329.
Article contents
Low-Dimensional Description of Pulses under the Action of Global Feedback Control
Published online by Cambridge University Press: 29 February 2012
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.
- Type
- Research Article
- Information
- Mathematical Modelling of Natural Phenomena , Volume 7 , Issue 2: Solitary waves , 2012 , pp. 83 - 94
- Copyright
- © EDP Sciences, 2012
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