Pattern formation in systems with multiple delayed feedbacks
Pattern Formation and Solitons
2015-06-19 v1 Mathematical Physics
math.MP
Adaptation and Self-Organizing Systems
Chaotic Dynamics
Optics
Abstract
Dynamical systems with complex delayed interactions arise commonly when propagation times are significant, yielding complicated oscillatory instabilities. In this Letter, we introduce a class of systems with multiple, hierarchically long time delays, and using a suitable space-time representation we uncover features otherwise hidden in their temporal dynamics. The behaviour in the case of two delays is shown to ''encode'' two-dimensional spiral defects and defects turbulence. A multiple scale analysis sets the equivalence to a complex Ginzburg-Landau equation, and a novel criterium for the attainment of the long-delay regime is introduced. We also demonstrate this phenomenon for a semiconductor laser with two delayed optical feedbacks.
Cite
@article{arxiv.1403.3585,
title = {Pattern formation in systems with multiple delayed feedbacks},
author = {Serhiy Yanchuk and Giovanni Giacomelli},
journal= {arXiv preprint arXiv:1403.3585},
year = {2015}
}