Product dynamics for homoclinic attractors

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Product dynamics for homoclinic attractors

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dc.contributor.author Ashwin, Peter en_GB
dc.contributor.author Field, Michael en_GB
dc.contributor.department University of Exeter; University of Houston en_GB
dc.date.accessioned 2008-03-11T16:16:54Z en_GB
dc.date.accessioned 2011-01-25T10:33:12Z en_US
dc.date.accessioned 2013-03-20T12:32:27Z
dc.date.issued 2005 en_GB
dc.description.abstract Heteroclinic 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.citation 461 (2053), pp. 155-177 en_GB
dc.identifier.doi doi:10.1098/rspa.2004.1362 en_GB
dc.identifier.uri http://hdl.handle.net/10036/20299 en_GB
dc.language.iso en en_GB
dc.publisher Royal Society en_GB
dc.relation.url http://dx.doi.org/10.1098/rspa.2004.1362 en_GB
dc.relation.url http://publishing.royalsociety.org/index.cfm?page=1086# en_GB
dc.subject Milnor attractor en_GB
dc.subject heteroclinic cycle en_GB
dc.subject connection selection en_GB
dc.title Product dynamics for homoclinic attractors en_GB
dc.type Article en_GB
dc.type Preprint en_GB
dc.date.available 2008-03-11T16:16:54Z en_GB
dc.date.available 2011-01-25T10:33:12Z en_US
dc.date.available 2013-03-20T12:32:27Z
dc.identifier.issn 1364-5021 en_GB
dc.identifier.issn 1471-2946 en_GB
dc.description Copyright © 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.2004.1362 en_GB
dc.identifier.journal Proceedings of the Royal Society A en_GB


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