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Chaos in a low-order model of magnetoconvection

Rucklidge, A.M. (1993) Chaos in a low-order model of magnetoconvection. Physica D: Nonlinear Phenomena, 62 (1-4). pp. 323-337. ISSN 0167-2789


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In the limit of tall, thin rolls, weakly nonlinear convection in a vertical magnetic field is described by an asymptotically exact third-order set of ordinary differential equations. These equations are shown here to have three codimension-two bifurcation points: a Takens-Bogdanov bifurcation, at which a gluing bifurcation is created; a point at which the gluing bifurcation is replaced by a pair of homoclinic explosions between which there are Lorenz-like chaotic trajectories; and a new type of bifurcation point at which the first of a cascade of period-doubling bifurcation lines originates. The last two bifurcation points are analysed in terms of a one-dimensional map. The equations also have a T-point, at which there is a heteroclinic connection between a saddle and a pair of saddle-foci; emerging from this point is a line of Shil'nikov bifurcations, involving homoclinic connections to a saddle-focus.

Item Type: Article
Copyright, Publisher and Additional Information: Copyright © 1993- Elsevier Science Publishers B.V. This is an author produced version of an article published in Physica D: Nonlinear Phenomena. This paper has been peer-reviewed but does not include the final publisher proof-corrections or journal pagination.
Keywords: magnetoconvection, Shimizu-Morioka model, homoclinical bifurcations, Lorenz map, chaos
Institution: The University of Leeds
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: 06 Feb 2006
Last Modified: 07 Jun 2014 02:47
Published Version: http://dx.doi.org/10.1016/0167-2789(93)90291-8
Status: Published
Refereed: Yes
Identification Number: 10.1016/0167-2789(93)90291-8
URI: http://eprints.whiterose.ac.uk/id/eprint/975

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