Two-state intermittency near a symmetric interaction of saddle-node and Hopf bifurcations: a case study from dynamo theory

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Two-state intermittency near a symmetric interaction of saddle-node and Hopf bifurcations: a case study from dynamo theory

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dc.contributor.author Ashwin, Peter en_GB
dc.contributor.author Rucklidge, Alastair M. en_GB
dc.contributor.author Sturman, Rob en_GB
dc.contributor.department University of Exeter; University of Leeds en_GB
dc.date.accessioned 2008-03-06T13:37:35Z en_GB
dc.date.accessioned 2011-01-25T10:33:53Z en_US
dc.date.accessioned 2013-03-20T12:27:55Z
dc.date.issued 2004 en_GB
dc.description.abstract We 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.citation 194 (1-2), pp. 30-48 en_GB
dc.identifier.doi 10.1016/j.physd.2004.02.002 en_GB
dc.identifier.uri http://hdl.handle.net/10036/19972 en_GB
dc.language.iso en en_GB
dc.publisher Elsevier en_GB
dc.relation.url http://dx.doi.org/10.1016/j.physd.2004.02.002 en_GB
dc.subject dynamo theory en_GB
dc.subject bifurcation with symmetry en_GB
dc.subject intermittency en_GB
dc.subject cycling chaos en_GB
dc.title Two-state intermittency near a symmetric interaction of saddle-node and Hopf bifurcations: a case study from dynamo theory en_GB
dc.type Article en_GB
dc.type Preprint en_GB
dc.date.available 2008-03-06T13:37:35Z en_GB
dc.date.available 2011-01-25T10:33:53Z en_US
dc.date.available 2013-03-20T12:27:55Z
dc.identifier.issn 0167-2789 en_GB
dc.description Copyright © 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.2004.02.002 en_GB
dc.identifier.journal Physica D en_GB


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