Kirk, V, Lane, E, Postlethwaite, CM et al. (2 more authors) (2010) A mechanism for switching near a heteroclinic network. Dynamical Systems, 25 (3). 323 - 349 . ISSN 1468-9367
Abstract
We describe an example of a robust heteroclinic network for which nearby orbits exhibit irregular but sustained switching between the various sub-cycles in the network. The mechanism for switching is the presence of spiralling due to complex eigenvalues in the flow linearized about one of the equilibria common to all cycles in the network. We construct and use return maps to investigate the asymptotic stability of the network, and show that switching is ubiquitous near the network. Some of the unstable manifolds involved in the network are two-dimensional; we develop a technique to account for all trajectories on those manifolds. A simple numerical example illustrates the rich dynamics that can result from the interplay between the various cycles in the network.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2010 Taylor & Francis. This is an author produced version of a paper published in Dynamical Systems. Reproduced in accordance with the publisher's self-archiving policy. |
Keywords: | heteroclinic network, switching, heteroclinic cycle, symmetry-breaking, asymptotic stability, homoclinic cycles, bifurcations, dynamics, systems, attractors, orbits, chaos |
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: | Symplectic Publications |
Date Deposited: | 12 Oct 2011 13:12 |
Last Modified: | 16 Sep 2016 14:08 |
Published Version: | http://dx.doi.org/10.1080/14689361003779134 |
Status: | Published |
Publisher: | Taylor & Francis |
Refereed: | Yes |
Identification Number: | 10.1080/14689361003779134 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:43325 |