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Mathematics > Dynamical Systems

arXiv:2210.02211 (math)
[Submitted on 5 Oct 2022]

Title:Equivariant Pyragas control of discrete waves

Authors:Babette de Wolff
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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.
Subjects: Dynamical Systems (math.DS)
MSC classes: 34K20, 34K35, 93C23, 37C81
Cite as: arXiv:2210.02211 [math.DS]
  (or arXiv:2210.02211v1 [math.DS] for this version)
  https://doi.org/10.48550/arXiv.2210.02211

Submission history

From: Babette de Wolff [view email]
[v1] Wed, 5 Oct 2022 12:38:46 UTC (141 KB)
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