Dynamics of a time-delayed relay system

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dc.contributor.authorIlling, Lucasen
dc.contributor.authorRyan, Pierceen
dc.contributor.authorAmann, Andreasen
dc.contributor.funderIrish Research Councilen
dc.contributor.funderMcAfeeen
dc.date.accessioned2024-02-09T14:48:37Z
dc.date.available2024-02-09T14:48:37Z
dc.date.issued2024-01-23en
dc.description.abstractWe 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.en
dc.description.sponsorshipIrish Research Council / McAfee (Award No. EBPPG/2018/269)en
dc.description.statusPeer revieweden
dc.description.versionPublished Versionen
dc.format.mimetypeapplication/pdfen
dc.identifier.articleid014223en
dc.identifier.citationIlling, L., Ryan, P. and Amann, A. (2024) 'Dynamics of a time-delayed relay system', Physical Review E, 109(1), 014223 (12pp). doi: https://doi.org/10.1103/PhysRevE.109.014223en
dc.identifier.doihttps://doi.org/10.1103/PhysRevE.109.014223en
dc.identifier.endpage12en
dc.identifier.issn2470-0045en
dc.identifier.issn2470-0053en
dc.identifier.issued1en
dc.identifier.journaltitlePhysical Review Een
dc.identifier.startpage1en
dc.identifier.urihttps://hdl.handle.net/10468/15550
dc.identifier.volume109en
dc.language.isoenen
dc.publisherAmerican Physical Societyen
dc.relation.projectEBPPG/2018/269en
dc.rights© 2024, American Physical Society. All rights reserved.en
dc.subjectTime-delayed relay systemen
dc.subjectFeedback systems with relaysen
dc.subjectMultirhythmicityen
dc.titleDynamics of a time-delayed relay systemen
dc.typeArticle (peer-reviewed)en
oaire.citation.issue1en
oaire.citation.volume109en
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