Robust bursting to the origin: heteroclinic cycles with maximal symmetry equilibria

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Robust bursting to the origin: heteroclinic cycles with maximal symmetry equilibria

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dc.contributor.author Hawker, David en_GB
dc.contributor.author Ashwin, Peter en_GB
dc.contributor.department University of Exeter en_GB
dc.date.accessioned 2008-04-04T15:12:29Z en_GB
dc.date.accessioned 2011-01-25T10:33:24Z en_US
dc.date.accessioned 2013-03-20T12:25:51Z
dc.date.issued 2005 en_GB
dc.description.abstract Robust attracting heteroclinic cycles have been found in many models of dynamics with symmetries. In all previous examples, robust heteroclinic cycles appear between a number of symmetry broken equilibria. In this paper we examine the first example where there are robust attracting heteroclinic cycles that include the origin, ie a point with maximal symmetry. The example we study is for vector fields on R3 with (Z2)3 symmetry. We list all possible generic (codimension one) local and global bifurcations by which this cycle can appear as an attractor; these include a resonance bifurcation from a limit cycle, direct bifurcation from a stable origin and direct bifurcation from other and more familiar robust heteroclinic cycles. en_GB
dc.identifier.citation 15 (9), pp. 2819-2832 en_GB
dc.identifier.doi 10.1142/S0218127405013708 en_GB
dc.identifier.uri http://hdl.handle.net/10036/22375 en_GB
dc.language.iso en en_GB
dc.publisher World Scientific Publishing Company en_GB
dc.relation.url http://dx.doi.org/10.1142/S0218127405013708 en_GB
dc.subject heteroclinic cycles en_GB
dc.subject robust en_GB
dc.subject bifurcation en_GB
dc.subject stability en_GB
dc.subject symmetry en_GB
dc.title Robust bursting to the origin: heteroclinic cycles with maximal symmetry equilibria en_GB
dc.type Article en_GB
dc.type Preprint en_GB
dc.date.available 2008-04-04T15:12:29Z en_GB
dc.date.available 2011-01-25T10:33:24Z en_US
dc.date.available 2013-03-20T12:25:51Z
dc.identifier.issn 0218-1274 en_GB
dc.description Preprint version of an article published in International Journal of Bifurcation and Chaos, 15, 9, 2005, pp. 2819-2832. DOI: 10.1142/S0218127405013708 © copyright World Scientific Publishing Company. http://www.worldscinet.com/ijbc/ijbc.shtml en_GB
dc.identifier.journal International Journal of Bifurcation and Chaos en_GB


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