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Infinities of stable periodic orbits in systems of coupled oscillators

Ashwin, P., Rucklidge, A.M. and Sturman, R. (2002) Infinities of stable periodic orbits in systems of coupled oscillators. Physical Review E, 66 (3 (art). pp. 1-4. ISSN 1063-651X

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Abstract

We consider the dynamical behavior of coupled oscillators with robust heteroclinic cycles between saddles that may be periodic or chaotic. We differentiate attracting cycles into types that we call phase resetting and free running depending on whether the cycle approaches a given saddle along one or many trajectories. At loss of stability of attracting cycling, we show in a phase-resetting example the existence of an infinite family of stable periodic orbits that accumulate on the cycling, whereas for a free-running example loss of stability of the cycling gives rise to a single quasiperiodic or chaotic attractor.

Item Type: Article
Copyright, Publisher and Additional Information: Readers may view, browse and/or download material for temporary copying purposes only, provided these uses are for non-commercial personal purposes. Except as provided by law, this material may not be further reproduced, distributed, transmitted, modified, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the publisher. "Reprinted wih permission from Ashwin P, Rucklidge AM, and Sturman R, Physical Review E, 66 art. No 035201, Part 2A, pp1-4, September 2002" © 2002 The American Physical Society
Academic Units: The University of Leeds > Faculty of Maths and Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds)
Depositing User: A. M. Rucklidge
Date Deposited: 11 Nov 2004
Last Modified: 08 Feb 2013 17:06
Published Version: http://link.aps.org/abstract/PRE/v66/e035201
Status: Published
Refereed: Yes
Identification Number: 10.1103/PhysRevE.66.035201
URI: http://eprints.whiterose.ac.uk/id/eprint/177

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