The effect of symmetry breaking on the dynamics near a structurally stable heteroclinic cycle between equilibria and a periodic orbit

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dc.creatorKirk, Vivien
dc.creatorRucklidge, Alastair M.
dc.date2006-08-01
dc.date2008-05-07
dc.date.accessioned2026-07-07T09:37:22Z
dc.date.available2026-07-07T09:37:22Z
dc.descriptionThe effect of small forced symmetry breaking on the dynamics near a structurally stable heteroclinic cycle connecting two equilibria and a periodic orbit is investigated. This type of system is known to exhibit complicated, possibly chaotic dynamics including irregular switching of sign of various phase space variables, but details of the mechanisms underlying the complicated dynamics have not previously been investigated. We identify global bifurcations that induce the onset of chaotic dynamics and switching near a heteroclinic cycle of this type, and by construction and analysis of approximate return maps, locate the global bifurcations in parameter space. We find there is a threshold in the size of certain symmetry-breaking terms below which there can be no persistent switching. Our results are illustrated by a numerical example.
dc.description43 pages, 14 figures. Full resolution version available on http://www.maths.leeds.ac.uk/~alastair/papers/KR_switching_abs.html
dc.identifierhttps://arxiv.org/abs/nlin/0608001
dc.identifierhttp://arxiv.org/abs/nlin/0608001
dc.identifierDynamical Systems, Vol. 23, No. 1, March 2008, 43-74
dc.identifierdoi:10.1080/14689360701709088
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/160437
dc.subjectChaotic Dynamics
dc.titleThe effect of symmetry breaking on the dynamics near a structurally stable heteroclinic cycle between equilibria and a periodic orbit
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