Weak tracking in nonautonomous chaotic systems

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dc.contributor.authorAlkhayuon, Hassan
dc.contributor.authorAshwin, Peter
dc.contributor.funderEnterprise Irelanden
dc.contributor.funderLaya Healthcare, Irelanden
dc.contributor.funderHorizon 2020en
dc.contributor.funderH2020 Marie Skłodowska-Curie Actionsen
dc.date.accessioned2020-12-16T16:39:09Z
dc.date.available2020-12-16T16:39:09Z
dc.date.issued2020-11-19
dc.date.updated2020-12-16T16:25:10Z
dc.description.abstractPrevious 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.sponsorshipEnterprise Ireland and Laya Healthcare (Grant Agreement No. 20190771)en
dc.description.statusPeer revieweden
dc.description.versionPublished Versionen
dc.format.mimetypeapplication/pdfen
dc.identifier.articleid52210en
dc.identifier.citationAlkhayuon, H. and Ashwin, P. (2020) 'Weak tracking in nonautonomous chaotic systems', Physical Review E, 102 (5), 052210 (7 pp). doi: 10.1103/PhysRevE.102.052210en
dc.identifier.doi10.1103/PhysRevE.102.052210en
dc.identifier.eissn2470-0053
dc.identifier.endpage7en
dc.identifier.issn2470-0045
dc.identifier.issued5en
dc.identifier.journaltitlePhysical Review Een
dc.identifier.startpage1en
dc.identifier.urihttps://hdl.handle.net/10468/10839
dc.identifier.volume102en
dc.language.isoenen
dc.publisherAmerican Physical Societyen
dc.relation.projectinfo:eu-repo/grantAgreement/EC/H2020::MSCA-ITN-ETN/643073/EU/Critical Transitions in Complex Systems/CRITICSen
dc.relation.urihttps://link.aps.org/doi/10.1103/PhysRevE.102.052210
dc.rights© 2020 American Physical Societyen
dc.subjectChaotic systemsen
dc.subjectChaotic attractorsen
dc.subjectInduced transitionsen
dc.subjectNon-autonomous systemen
dc.subjectNonautonomous chaotic systemsen
dc.subjectParameter changesen
dc.subjectParameter shiftsen
dc.subjectPullback attractorsen
dc.subjectUnstable periodic orbitsen
dc.titleWeak tracking in nonautonomous chaotic systemsen
dc.typeArticle (peer-reviewed)en
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