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Kirk, V and Rucklidge, AM orcid.org/0000-0003-2985-0976 (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
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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | (c) 2008 Taylor & Francis. This is an Accepted Manuscript of an article published by Taylor & Francis in Dynamical Systems on 1 March 2008, available online: https://doi.org/10.1080/14689360701709088. |
Keywords: | ASYMPTOTIC STABILITY; HOMOCLINIC CYCLES; SYSTEMS; BIFURCATIONS; ATTRACTORS; CONVECTION; NETWORK |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Repository Administrator York |
Date Deposited: | 05 Sep 2019 10:33 |
Last Modified: | 23 Jun 2023 21:32 |
Status: | Published |
Publisher: | Taylor & Francis |
Refereed: | Yes |
Identification Number: | 10.1080/14689360701709088 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:74784 |
Available Versions of this Item
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The effect of symmetry breaking on the dynamics near a structurally stable heteroclinic cycle between equilibria and a periodic orbit. (deposited 30 Jul 2008 11:47)
- The effect of symmetry breaking on the dynamics near a structurally stable heteroclinic cycle between equilibria and a periodic orbit. (deposited 05 Sep 2019 10:33) [Currently Displayed]