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dc.contributor.authorAshwin, Peteren_GB
dc.contributor.authorField, Michaelen_GB
dc.contributor.departmentUniversity of Exeter; University of Houstonen_GB
dc.date.accessioned2008-03-11T16:16:54Zen_GB
dc.date.accessioned2011-01-25T10:33:12Zen_GB
dc.date.accessioned2013-03-20T12:32:27Z
dc.date.issued2005en_GB
dc.description.abstractHeteroclinic cycles may occur as structurally stable asymptotically stable attractors if there are invariant subspaces or symmetries of a dynamical system. Even for cycles between equilibria, it may be difficult to obtain results on the generic behaviour of trajectories converging to the cycle. For more-complicated cycles between chaotic sets, the non-trivial dynamics of the 'nodes' can interact with that of the 'connections'. This paper focuses on some of the simplest problems for such dynamics where there are direct products of an attracting homoclinic cycle with various types of dynamics. Using a precise analytic description of a general planar homoclinic attractor, we are able to obtain a number of results for direct product systems. We show that for flows that are a product of a homoclinic attractor and a periodic orbit or a mixing hyperbolic attractor, the product of the attractors is a minimal Milnor attractor for the product. On the other hand, we present evidence to show that for the product of two homoclinic attractors, typically only a small subset of the product of the attractors is an attractor for the product system.en_GB
dc.identifier.citation461 (2053), pp. 155-177en_GB
dc.identifier.doidoi:10.1098/rspa.2004.1362en_GB
dc.identifier.urihttp://hdl.handle.net/10036/20299en_GB
dc.language.isoenen_GB
dc.publisherRoyal Societyen_GB
dc.relation.urlhttp://dx.doi.org/10.1098/rspa.2004.1362en_GB
dc.relation.urlhttp://publishing.royalsociety.org/index.cfm?page=1086#en_GB
dc.subjectMilnor attractoren_GB
dc.subjectheteroclinic cycleen_GB
dc.subjectconnection selectionen_GB
dc.titleProduct dynamics for homoclinic attractorsen_GB
dc.typeArticleen_GB
dc.date.available2008-03-11T16:16:54Zen_GB
dc.date.available2011-01-25T10:33:12Zen_GB
dc.date.available2013-03-20T12:32:27Z
dc.identifier.issn1364-5021en_GB
dc.identifier.issn1471-2946en_GB
dc.descriptionCopyright © 2004 The Royal Society. NOTICE: This is the author’s version of a work accepted for publication by The Royal Society. The definitive version was subsequently published in Proceedings of the Royal Society A, Vol 461, Number 2053, online 5 October 2004 and in print 5 January 2005, DOI:10.1098/rspa.2004.1362en_GB
dc.identifier.journalProceedings of the Royal Society Aen_GB


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