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)
Official URL: http://www.journals.royalsoc.ac.uk/(ishg5e55p2ildl...
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.
|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|
|Deposited By:||Irene Moroz|
|Deposited On:||01 Dec 2006|
|Last Modified:||29 May 2015 18:22|
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