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: firstname.lastname@example.org
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.