The Hide, Skeldon, Acheson dynamo revisited

@article{citeulike:2776236, 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.}, author = {Moroz, Irene M. }, citeulike-article-id = {2776236}, doi = {10.1098/rspa.2006.1758}, journal = {Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences}, keywords = {dynamo}, month = {January}, number = {2077}, pages = {113--130}, posted-at = {2008-05-09 17:13:07}, priority = {2}, title = {The Hide, Skeldon, Acheson dynamo revisited}, url = {http://dx.doi.org/10.1098/rspa.2006.1758}, volume = {463}, year = {2007} }

TY - JOUR ID - citeulike:2776236 L3 - citeulike-article-id:2776236 TI - The Hide, Skeldon, Acheson dynamo revisited JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences VL - 463 IS - 2077 SP - 113 EP - 130 N2 - 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. KW - dynamo AU - Moroz, Irene PY - 2007/01// UR - http://dx.doi.org/10.1098/rspa.2006.1758 ER -