Hypermeander of spirals: local bifurcations and statistical properties

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Hypermeander of spirals: local bifurcations and statistical properties

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dc.contributor.author Ashwin, Peter en_GB
dc.contributor.author Melbourne, Ian en_GB
dc.contributor.author Nicol, Matthew en_GB
dc.contributor.department University of Exeter; University of Houston; University of Surrey en_GB
dc.date.accessioned 2008-03-06T15:19:48Z en_GB
dc.date.accessioned 2011-01-25T10:33:11Z en_US
dc.date.accessioned 2013-03-20T12:32:16Z
dc.date.issued 2001 en_GB
dc.description.abstract In both experimental studies and numerical simulations of waves in excitable media, rigidly rotating spiral waves are observed to undergo transitions to complicated spatial dynamics with long-term Brownian-like motion of the spiral tip. This phenomenon is known as hypermeander. In this paper, we review a number of recent results on dynamics with noncompact group symmetries and make the case that hypermeander may occur at a codimension two bifurcation from a rigidly rotating spiralwave.Our predictions are based on center bundle reduction (Sandstede, Scheel and Wulff), and on central limit theorems and invariance principles for group extensions of hyperbolic dynamical systems. These predictions are confirmed by numerical simulations of the center bundle equations. en_GB
dc.identifier.citation 156 (3-4), pp. 364-382 en_GB
dc.identifier.doi 10.1016/S0167-2789(01)00296-2 en_GB
dc.identifier.uri http://hdl.handle.net/10036/19993 en_GB
dc.language.iso en en_GB
dc.publisher Elsevier en_GB
dc.relation.url http://dx.doi.org/10.1016/S0167-2789(01)00296-2 en_GB
dc.subject hypermeander en_GB
dc.subject bifurcation en_GB
dc.subject centre bundle en_GB
dc.subject spiral wave en_GB
dc.subject deterministic Brownian motion en_GB
dc.subject invariance principle en_GB
dc.title Hypermeander of spirals: local bifurcations and statistical properties en_GB
dc.type Article en_GB
dc.type Preprint en_GB
dc.date.available 2008-03-06T15:19:48Z en_GB
dc.date.available 2011-01-25T10:33:11Z en_US
dc.date.available 2013-03-20T12:32:16Z
dc.identifier.issn 0167-2789 en_GB
dc.description Copyright © 2001 Elsevier. NOTICE: This is the author’s version of a work accepted for publication by Elsevier. Changes resulting from the publishing process, including peer review, editing, corrections, structural formatting and other quality control mechanisms, may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Physica D, Vol 156, Issues 3-4, 2001, DOI: 10.1016/S0167-2789(01)00296-2 en_GB
dc.identifier.journal Physica D en_GB


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