| Abstract: | We study in great detail a system of three first-order ordinary differential equations describing a homopolar disk dynamo (HDD). This system displays a large variety of behaviors, both regular and chaotic. Existence of periodic solutions is proved for certain ranges of parameters. Stability criteria for periodic solutions are given. The nonintegrability aspects of the HDD system are studied by investigating analytically the singularity structure of the system in the complex domain. Coexisting attractors (including period-doubling sequence) and coexisting strange attractors appear in some parametric regimes. The gluing of strange attractors and the ungluing of a strange attractor are also shown to occur. A period of bifurcation leading to chaos, not observed for other chaotic systems, is shown to characterize the chaotic behavior in some parametric ranges. The limiting case of the Lorenz system is also studied and is related to HDD. |
