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On a codimension-three bifurcation arising in a simple dynamo model

Skeldon, AC and Moroz, IM (1998) On a codimension-three bifurcation arising in a simple dynamo model Physica D-Nonlinear Phenomena, 117 (1-4). 117 - 127. ISSN 0167-2789

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Abstract

In this paper we investigate the dynamics associated with a degenerate codimension-two Takens-Bogdanov bifurcation which arises in a recently derived model for self-exciting dynamo action introduced by Hide et al. [R. Hide, A.C. Skeldon, D.J. Acheson, A study of two novel self-exciting single-disk homopolar dynamos: theory, Proc. R. Soc. Lond. A 452 (1996) 1369-1395]. The general unfolding of such a codimension-three bifurcation has already been discussed in an abstract setting by Li and Rousseau [Codimension-2 symmetric homoclinic bifurcations and application to 1:2 resonance, Can J. Math. 42 (1990) 191-212].Here we describe the unfolding scenario in the context of the dynamo problem. In particular we compare the behaviour predicted by the normal form analysis with a bifurcation study of the full dynamo equations in the neighbourhood of the codimension-three point.

Item Type: Article
Additional Information: NOTICE: this is the author’s version of a work that was accepted for publication in PHYSICA D. Changes resulting from the publishing process, such as 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, 117(1-4), June 1998, DOI 10.1016/S0167-2789(97)00316-3.
Uncontrolled Keywords: Takens-Bogdanov, codimension-three bifurcation, dynamo model
Divisions: Faculty of Engineering and Physical Sciences > Mathematics
Depositing User: Symplectic Elements
Date Deposited: 01 Feb 2012 10:04
Last Modified: 23 Sep 2013 18:57
URI: http://epubs.surrey.ac.uk/id/eprint/72363

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