Weak tracking in nonautonomous chaotic systems

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dc.contributor.author Alkhayuon, Hassan
dc.contributor.author Ashwin, Peter
dc.date.accessioned 2020-12-16T16:39:09Z
dc.date.available 2020-12-16T16:39:09Z
dc.date.issued 2020-11-19
dc.identifier.citation Alkhayuon, H. and Ashwin, P. (2020) 'Weak tracking in nonautonomous chaotic systems', Physical Review E, 102 (5), 052210 (7 pp). doi: 10.1103/PhysRevE.102.052210 en
dc.identifier.volume 102 en
dc.identifier.issued 5 en
dc.identifier.startpage 1 en
dc.identifier.endpage 7 en
dc.identifier.issn 2470-0045
dc.identifier.uri http://hdl.handle.net/10468/10839
dc.identifier.doi 10.1103/PhysRevE.102.052210 en
dc.description.abstract Previous studies have shown that rate-induced transitions can occur in pullback attractors of systems subject to “parameter shifts” between two asymptotically steady values of a system parameter. For cases where the attractors limit to equilibrium or periodic orbit in past and future limits of such an nonautonomous systems, these can occur as the parameter change passes through a critical rate. Such rate-induced transitions for attractors that limit to chaotic attractors in past or future limits has been less examined. In this paper, we identify a new phenomenon is associated with more complex attractors in the future limit: weak tracking, where a pullback attractor of the system limits to a proper subset of an attractor of the future limit system. We demonstrate weak tracking in a nonautonomous Rössler system, and argue there are infinitely many critical rates at each of which the pullback attracting solution of the system tracks an embedded unstable periodic orbit of the future chaotic attractor. We also state some necessary conditions that are needed for weak tracking. en
dc.description.sponsorship Enterprise Ireland and Laya Healthcare (Grant Agreement No. 20190771) en
dc.format.mimetype application/pdf en
dc.language.iso en en
dc.publisher American Physical Society en
dc.relation.uri https://link.aps.org/doi/10.1103/PhysRevE.102.052210
dc.rights © 2020 American Physical Society en
dc.subject Chaotic systems en
dc.subject Chaotic attractors en
dc.subject Induced transitions en
dc.subject Non-autonomous system en
dc.subject Nonautonomous chaotic systems en
dc.subject Parameter changes en
dc.subject Parameter shifts en
dc.subject Pullback attractors en
dc.subject Unstable periodic orbits en
dc.title Weak tracking in nonautonomous chaotic systems en
dc.type Article (peer-reviewed) en
dc.internal.authorcontactother Hassan Alkhayuon, School of Mathematical Sciences, University College Cork, Cork, Ireland. +353-21-490-3000 Email: hassan.alkhayuon@ucc.ie en
dc.internal.availability Full text available en
dc.date.updated 2020-12-16T16:25:10Z
dc.description.version Published Version en
dc.internal.rssid 547794310
dc.contributor.funder Enterprise Ireland en
dc.contributor.funder Laya Healthcare, Ireland en
dc.contributor.funder Horizon 2020 en
dc.contributor.funder H2020 Marie Skłodowska-Curie Actions en
dc.description.status Peer reviewed en
dc.identifier.journaltitle Physical Review E en
dc.internal.copyrightchecked Yes
dc.internal.licenseacceptance Yes en
dc.internal.IRISemailaddress hassan.alkhayuon@ucc.ie en
dc.identifier.articleid 52210 en
dc.relation.project info:eu-repo/grantAgreement/EC/H2020::MSCA-ITN-ETN/643073/EU/Critical Transitions in Complex Systems/CRITICS en
dc.identifier.eissn 2470-0053


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