Equivariant Pyragas control of discrete waves

2022/10/05 by Babette A. J. de Wolff, de Wolff, Babette
Computer Science · Physics and Astronomy · #34K20 #34K35 #37C81 #93C23 #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2210.02211

openalex publication_date 2022/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Equivariant Pyragas control is a delayed feedback method that aims to stabilize spatio-temporal patterns in systems with symmetries. In this article, we apply equivariant Pyragas control to discrete waves, which are periodic solutions that have a finite number of spatio-temporal symmetries. We prove sufficient conditions under which a discrete wave can be stabilized via equivariant Pyragas control. The result isapplicable to a broad class of discrete waves, including discrete waves that are far away from a bifurcation point. Key ingredients of the proof are an adaptation of Floquet theory to systems with symmetries, and the use of characteristic matrix functions to reduce the infinite dimensional eigenvalue problem to a one dimensional zero finding problem.

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