Relative equilibria and relative periodic solutions in systems with time-delay and S¹ symmetry

2013/06/14 by Serhiy Yanchuk, Yanchuk, Serhiy, Jan Sieber +1
Computer Science · Engineering · Mathematics · Physics and Astronomy · #34Kxx #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Dynamics and Pattern Formation #Optics (physics.optics) #Quantum chaos and dynamical systems #Semiconductor Lasers and Optical Devices #math-ph #math.MP #msc:34Kxx #nlin.CD #physics.optics

paper · pdf · doi:10.48550/arxiv.1306.3327

openalex publication_date 2013/06/14 · openalex created_date 2016/06/24 · arxiv created 2016/12/03 · arxiv updated 2016/12/06 · openalex updated_date 2026/07/28

Abstract

We study properties of basic solutions in systems with dime delays and S¹-symmetry. Such basic solutions are relative equilibria (CW solutions) and relative periodic solutions (MW solutions). It follows from the previous theory that the number of CW solutions grows generically linearly with time delay τ. Here we show, in particular, that the number of relative periodic solutions grows generically as τ² when delay increases. Thus, in such systems, the relative periodic solutions are more abundant than relative equilibria. The results are directly applicable to, e.g., Lang-Kobayashi model for the lasers with delayed feedback. We also study stability properties of the solutions for large delays.

Citations

• External optical feedback effects on semiconductor injection laser properties

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