The Mathematical Institute, University of Oxford, Eprints Archive

The Hide,Skeldon,Acheson dynamo revisited

Moroz, Irene M. (2007) The Hide,Skeldon,Acheson dynamo revisited. Proceedings of the Royal Society A, 463 (2077). pp. 113-130. ISSN 1364-5021 (Paper) 1471-2946 (Online)

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Official URL: http://www.journals.royalsoc.ac.uk/(ishg5e55p2ildl...

Abstract

Hide et al. (Hide, Skeldon & Acheson 1996 Proc. R. Soc. A452, 1369–1395) introduced a nonlinear system of three coupled ordinary differential equations to model a self-exciting Faraday disk homopolar dynamo. A very small selection of its possible behaviours was presented in that paper. Subsequent studies have extended the system to incorporate the effects of a nonlinear motor, an external battery and magnetic field, the coupling of two or more identical dynamos together, among other things. In this paper, we return to the original model with a view to perform a more extensive analysis of the Hide et al. dynamo. For the first time, we present bifurcation transition diagrams, so that the two examples of chaotic dynamo action (shown in figure 9 in that paper) can now be placed into context. We exhibit the coexistence of multiple attractors and also identify the lowest order unstable periodic orbits pertaining to some specific cases.

Item Type:Article
Uncontrolled Keywords:unstable periodic orbits, dynamo models, bifurcations
Subjects:D - G > Geophysics
D - G > Dynamical systems and ergodic theory
O - Z > Ordinary differential equations
Research Groups:Oxford Centre for Industrial and Applied Mathematics
ID Code:448
Deposited By:Irene Moroz
Deposited On:01 Dec 2006
Last Modified:20 Jul 2009 14:21

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