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dc.contributor.authorAshwin, Peteren_GB
dc.contributor.authorRucklidge, Alastair M.en_GB
dc.contributor.authorSturman, Roben_GB
dc.contributor.departmentUniversity of Exeter; University of Leedsen_GB
dc.date.accessioned2008-03-06T13:37:35Zen_GB
dc.date.accessioned2011-01-25T10:33:53Zen_GB
dc.date.accessioned2013-03-20T12:27:55Z
dc.date.issued2004en_GB
dc.description.abstractWe consider a model of a Hopf bifurcation interacting as a codimension 2 bifurcation with a saddle-node on a limit cycle, motivated by a low-order model for magnetic activity in a stellar dynamo. This model consists of coupled interactions between a saddle-node and two Hopf bifurcations, where the saddle-node bifurcation is assumed to have global reinjection of trajectories. The model can produce chaotic behaviour within each of a pair of invariant subspaces, and also it can show attractors that are stuck-on to both of the invariant subspaces. We investigate the detailed intermittent dynamics for such an attractor, investigating the effect of breaking the symmetry between the two Hopf bifurcations, and observing that it can appear via blowout bifurcations from the invariant subspaces. We give a simple Markov chain model for the two-state intermittent dynamics that reproduces the time spent close to the invariant subspaces and the switching between the different possible invariant subspaces; this clarifes the observation that the proportion of time spent near the different subspaces depends on the average residence time and also on the probabilities of switching between the possible subspaces.en_GB
dc.identifier.citation194 (1-2), pp. 30-48en_GB
dc.identifier.doi10.1016/j.physd.2004.02.002en_GB
dc.identifier.urihttp://hdl.handle.net/10036/19972en_GB
dc.language.isoenen_GB
dc.publisherElsevieren_GB
dc.relation.urlhttp://dx.doi.org/10.1016/j.physd.2004.02.002en_GB
dc.subjectdynamo theoryen_GB
dc.subjectbifurcation with symmetryen_GB
dc.subjectintermittencyen_GB
dc.subjectcycling chaosen_GB
dc.titleTwo-state intermittency near a symmetric interaction of saddle-node and Hopf bifurcations: a case study from dynamo theoryen_GB
dc.typeArticleen_GB
dc.date.available2008-03-06T13:37:35Zen_GB
dc.date.available2011-01-25T10:33:53Zen_GB
dc.date.available2013-03-20T12:27:55Z
dc.identifier.issn0167-2789en_GB
dc.descriptionCopyright © 2004 Elsevier. NOTICE: This is the author’s version of a work accepted for publication by Elsevier. Changes resulting from the publishing process, including peer review, editing, corrections, structural formatting and other quality control mechanisms, may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Physica D, Vol 194, Issues 1-2, 2004, DOI:10.1016/j.physd.2004.02.002en_GB
dc.identifier.journalPhysica Den_GB


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