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Global bifurcations in the Takens-Bogdanov normal form with D_4 symmetry near the O(2) limit

Rucklidge, A.M. (2001) Global bifurcations in the Takens-Bogdanov normal form with D_4 symmetry near the O(2) limit. Physics Letters A, 284 (2-3). pp. 99-111. ISSN 0375-9601

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Abstract

The dynamics of the normal form of the Takens-Bogdanov bifurcation with D_4 symmetry is governed by a one-dimensional map near the gluing bifurcation and near the O(2) integrable limit, rather than the three-dimensional map one would expect. This great simplification allows a quantitative description of the bifurcation sequence through which stability is transfered between invariant subspaces.

Item Type: Article
Copyright, Publisher and Additional Information: Copyright © 2001 Elsevier Science Publishers B.V. This is an author produced version of an article published in Physics Letters A. This paper has been peer-reviewed but does not include the final publisher proof-corrections or journal pagination.
Keywords: gluing bifurcation, symmetry, chaos, magnetoconvection
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: 10 Feb 2006
Last Modified: 08 Feb 2013 17:02
Published Version: http://dx.doi.org/10.1016/S0375-9601(01)00276-6
Status: Published
Refereed: Yes
Identification Number: 10.1016/S0375-9601(01)00276-6
URI: http://eprints.whiterose.ac.uk/id/eprint/993

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