Math. Model. Nat. Phenom.
Volume 7, Number 2, 2012Solitary waves
|Page(s)||83 - 94|
|Published online||29 February 2012|
Low-Dimensional Description of Pulses under the Action of Global Feedback Control
Department of Mathematics, Technion – Israel Institute of
Technology Haifa, 32000, Israel
⋆ Corresponding author. E-mail: email@example.com
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.
Mathematics Subject Classification: 35B36 / 93B52
Key words: Ginzburg-Landau equation / delayed feedback control / finite-dimensional models / solitary waves
© EDP Sciences, 2012
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