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

Kirk, V. and Rucklidge, A.M. (2008) The effect of symmetry breaking on the dynamics near a structurally stable heteroclinic cycle between equilibria and a periodic orbit. Dynamical Systems, 23 (1). pp. 43-74. ISSN 1468-9367

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Abstract

The 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.

Item Type: Article
Copyright, Publisher and Additional Information: © 2008 Taylor & Francis Ltd. This is an author produced version of a paper published in March 2008. Uploaded in accordance with the publisher's self archiving policy.
Institution: The University of Leeds
Academic Units: The University of Leeds > Faculty of Maths and Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds)
Depositing User: Repository Administrator York
Date Deposited: 30 Jul 2008 11:47
Last Modified: 06 Jun 2014 19:51
Published Version: http://dx.doi.org/10.1080/14689360701709088
Status: Published
Publisher: Taylor & Francis Ltd
Refereed: Yes
Identification Number: 10.1080/14689360701709088
Related URLs:
URI: http://eprints.whiterose.ac.uk/id/eprint/3753

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