Moroz, Irene M. (2007) The Hide,Skeldon,Acheson dynamo revisited. Proceedings of the Royal Society A, 463 (2077). pp. 113130. ISSN 13645021 (Paper) 14712946 (Online)

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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 selfexciting 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:  29 May 2015 18:22 
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