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Destabilization by noise of tranverse perturbations to heteroclinic cycles: a simple model and an example from dynamo theory

Gog, J.R., Oprea, I., Proctor, M.R.E. and Rucklidge, A.M. (1999) Destabilization by noise of tranverse perturbations to heteroclinic cycles: a simple model and an example from dynamo theory. Proceedings of the Royal Society Series A: Mathematical Physical and Engineering Sciences, 455 (1992). pp. 4205-4222. ISSN 1471-2946

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Abstract

We show that transverse perturbations from structurally stable heteroclinic cycles can be destabilized by surprisingly small amounts of noise, even when each individual fixed point of the cycle is stable to transverse modes. A condition that favours this process is that the linearization of the dynamics in the transverse direction be characterized by a non-normal matrix. The phenomenon is illustrated by a simple two-dimensional switching model and by a simulation of a convectively driven dynamo.

Item Type: Article
Copyright, Publisher and Additional Information: Copyright © 1999 The Royal Society.
Keywords: transverse instability, noise-induced instability, non-normal dynamics, heteroclinic cycle, dynamo theory
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: 07 Feb 2006
Last Modified: 08 Feb 2013 17:02
Published Version: http://www.journals.royalsoc.ac.uk/openurl.asp?gen...
Status: Published
Refereed: Yes
Identification Number: 10.1098/rspa.1999.0498
URI: http://eprints.whiterose.ac.uk/id/eprint/987

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