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Three-dimensional forced-damped dynamical systems with rich dynamics : bifurcations, chaos and unbounded solutions

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dc.contributor.authorMiyaji, Tomoyuki
dc.contributor.authorOkamoto, Hisashi
dc.contributor.authorCraik, Alexander Duncan Davidson
dc.date.accessioned2016-09-09T23:34:03Z
dc.date.available2016-09-09T23:34:03Z
dc.date.issued2015
dc.identifier.citationMiyaji , T , Okamoto , H & Craik , A D D 2015 , ' Three-dimensional forced-damped dynamical systems with rich dynamics : bifurcations, chaos and unbounded solutions ' , Physica D: Nonlinear Phenomena , vol. In press . https://doi.org/10.1016/j.physd.2015.09.001en
dc.identifier.issn0167-2789
dc.identifier.otherPURE: 215638154
dc.identifier.otherPURE UUID: c05f01e4-57d6-485d-94f1-80bbf02c6acd
dc.identifier.otherRIS: urn:9842B9BD0D5D22E5B428ECCE76FA6B3C
dc.identifier.otherScopus: 84942112752
dc.identifier.otherWOS: 000364271600003
dc.identifier.urihttps://hdl.handle.net/10023/9468
dc.descriptionT.M. is supported by the Grant-in-Aid for JSPS Fellow No. 24·5312. H.O. is partially supported by JSPS KAKENHI 24244007.en
dc.description.abstractWe consider certain autonomous three-dimensional dynamical systems that can arise in mechanical and fluid-dynamical contexts. Extending a previous study in Craik and Okamoto (2002), to include linear forcing and damping, we find that the four-leaf structure discovered in that paper, and unbounded orbits, persist, but may now be accompanied by three distinct period-doubling cascades to chaos, and by orbits that approach stable equilibrium points. This rich structure is investigated both analytically and numerically, distinguishing three main cases determined by the damping and forcing parameter values.
dc.language.isoeng
dc.relation.ispartofPhysica D: Nonlinear Phenomenaen
dc.rightsCopyright © 2015 Published by Elsevier B.V. This work is made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://dx.doi.org/10.1016/j.physd.2015.09.001en
dc.subjectThree-dimensional dynamical systemen
dc.subjectPeriod-doubling cascades to chaosen
dc.subjectAsymptotic analysisen
dc.subjectLyapunov functionen
dc.subjectQA Mathematicsen
dc.subjectNDASen
dc.subject.lccQAen
dc.titleThree-dimensional forced-damped dynamical systems with rich dynamics : bifurcations, chaos and unbounded solutionsen
dc.typeJournal articleen
dc.description.versionPostprinten
dc.contributor.institutionUniversity of St Andrews. Applied Mathematicsen
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.identifier.doihttps://doi.org/10.1016/j.physd.2015.09.001
dc.description.statusPeer revieweden
dc.date.embargoedUntil2016-09-09


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