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  Dynamics of a time-delayed relay system

Illing, L., Ryan, P., Amann, A. (2024): Dynamics of a time-delayed relay system. - Physical Review E, 109, 1, 014223.
https://doi.org/10.1103/PhysRevE.109.014223

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 Creators:
Illing, Lucas1, Author
Ryan, Pierce1, Author
Amann, Andreas2, Author              
Affiliations:
1External Organizations, ou_persistent22              
2Potsdam Institute for Climate Impact Research, Potsdam, ou_persistent13              

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 Abstract: We study the dynamics of a piecewise-linear second-order delay differential equation that is representative of feedback systems with relays (switches) that actuate after a fixed delay. The system under study exhibits strong multirhythmicity, the coexistence of many stable periodic solutions for the same values of the parameters. We present a detailed study of these periodic solutions and their bifurcations. Starting from an integrodifferential model, we show how to reduce the system to a set of finite-dimensional maps. We then demonstrate that the parameter regions of existence of periodic solutions can be understood in terms of discontinuity-induced bifurcations and their stability is determined by smooth bifurcations. Using this technique, we are able to show that slowly oscillating solutions are always stable if they exist. We also demonstrate the coexistence of stable periodic solutions with quasiperiodic solutions.

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Language(s): eng - English
 Dates: 2024-01-232024-01-23
 Publication Status: Finally published
 Pages: 12
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Identifiers: DOI: 10.1103/PhysRevE.109.014223
MDB-ID: No data to archive
PIKDOMAIN: RD4 - Complexity Science
Organisational keyword: RD4 - Complexity Science
Research topic keyword: Nonlinear Dynamics
OATYPE: Green Open Access
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Title: Physical Review E
Source Genre: Journal, SCI, Scopus, p3
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Pages: - Volume / Issue: 109 (1) Sequence Number: 014223 Start / End Page: - Identifier: CoNE: https://publications.pik-potsdam.de/cone/journals/resource/150218
Publisher: American Physical Society (APS)