Numerical detection of synchronization phenomena in quasi-periodic solutions

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dc.date.accessioned2023-12-15T15:38:50Z
dc.date.available2023-12-15T15:38:50Z
dc.date.issued2023-10-05
dc.description.sponsorshipGefördert im Rahmen des Projekts DEALger
dc.identifierdoi:10.17170/kobra-202311309143
dc.identifier.urihttp://hdl.handle.net/123456789/15306
dc.language.isoeng
dc.relation.doidoi:10.1002/pamm.202300235
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 International*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/*
dc.subject.ddc620
dc.subject.swdSynchronisierungger
dc.subject.swdDynamisches Systemger
dc.subject.swdGrundfrequenzger
dc.subject.swdParametrisierungger
dc.titleNumerical detection of synchronization phenomena in quasi-periodic solutionseng
dc.typeAufsatz
dc.type.versionpublishedVersion
dcterms.abstractIn science and technology, dynamical systems can show so-called quasi-periodic solutions. These solutions are composed of two or more base frequencies. The solution in the time domain can be represented by an invariant manifold. To parametrize the invariant manifold, we choose the hyper-time parametrization. If quasi-periodic solutions branches are continued by means of a path continuation, the phenomenon of synchronization may occur. This is important, because the hyper-time parametrization is only valid, as long as the number of base frequencies remains unchanged. Therefore, it is essential to detect a parametrization to a synchronization point. Synchronization can happen in different types. We address the mechanism of suppression, where one base frequency becomes suppressed until its amplitude vanishes. This corresponds to the quasi-periodic solution ending in a Neimark–Sacker bifurcation. We present a method to derive a scalar measure from the quasi-periodic solution in the hyper-time parametrization, to detect an approach to a Neimark–Sacker bifurcation while continuing the solution branch.eng
dcterms.accessRightsopen access
dcterms.creatorSeifert, Alexander
dcterms.creatorBäuerle, Simon Andreas
dcterms.creatorHetzler, Hartmut
dcterms.source.articlenumbere202300235
dcterms.source.identifiereissn:1617-7061
dcterms.source.issueIssue 3
dcterms.source.journalProceedings in Applied Mathematics and Mechanics (PAMM)eng
dcterms.source.volumeVolume 23
kup.iskupfalse

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