White Rose University Consortium logo
University of Leeds logo University of Sheffield logo York University logo

A mechanism for switching near a heteroclinic network

Kirk, V, Lane, E, Postlethwaite, CM, Rucklidge, AM and Silber, M (2010) A mechanism for switching near a heteroclinic network. Dynamical Systems, 25 (3). 323 - 349 . ISSN 1468-9367


Download (691Kb)


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.

Item Type: Article
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
Institution: The University of Leeds
Academic Units: The University of Leeds > Faculty of Maths and Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds)
Depositing User: Symplectic Publications
Date Deposited: 12 Oct 2011 13:12
Last Modified: 08 Feb 2013 17:34
Published Version: http://dx.doi.org/10.1080/14689361003779134
Status: Published
Publisher: Taylor & Francis
Refereed: Yes
Identification Number: 10.1080/14689361003779134
Related URLs:
URI: http://eprints.whiterose.ac.uk/id/eprint/43325

Actions (repository staff only: login required)