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

Please use this identifier to cite or link to this item: http://hdl.handle.net/10036/19972

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Title: Two-state intermittency near a symmetric interaction of saddle-node and Hopf bifurcations: a case study from dynamo theory
Author: Ashwin, Peter
Rucklidge, Alastair M.
Sturman, Rob
Citation: 194 (1-2), pp. 30-48
Publisher: Elsevier
Journal: Physica D
Date Issued: 2004
URI: http://hdl.handle.net/10036/19972
DOI: 10.1016/j.physd.2004.02.002
Links: http://dx.doi.org/10.1016/j.physd.2004.02.002
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.
Type: Article
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
Keywords: dynamo theorybifurcation with symmetryintermittencycycling chaos
ISSN: 0167-2789


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