Stability of plane wave solutions in complex Ginzburg-Landau equation with delayed feedback
Dynamical Systems
2013-11-12 v1 Pattern Formation and Solitons
Abstract
We perform bifurcation analysis of plane wave solutions in one-dimensional cubic-quintic Ginzburg-Landau equation with delayed feedback. Our study reveals how multistability and snaking behavior of plane waves emerge as time delay is introduced. For intermediate values of the delay, bifurcation diagrams are obtained by a combination of analytical and numerical methods. For large delays, using an asymptotic approach we classify plane wave solutions into strongly unstable, weakly unstable, and stable. The results of analytical bifurcation analysis are in agreement with those obtained by direct numerical integration of the model equation.
Keywords
Cite
@article{arxiv.1311.2414,
title = {Stability of plane wave solutions in complex Ginzburg-Landau equation with delayed feedback},
author = {D. Puzyrev and S. Yanchuk and A. G. Vladimirov and S. V. Gurevich},
journal= {arXiv preprint arXiv:1311.2414},
year = {2013}
}