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The Hide, Skeldon, Acheson dynamo revisited

2006; Royal Society; Volume: 463; Issue: 2077 Linguagem: Inglês

10.1098/rspa.2006.1758

1471-2946

Irene M. Moroz,

Solar and Space Plasma Dynamics

Hide et al . (Hide, Skeldon & Acheson 1996 Proc. R. Soc. A 452 , 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.