Unstable periodic orbits in a four-dimensional Faraday disk dynamo

摘要

In this article, we return to a four-dimensional model for a self-exciting Faraday disk dynamo, originally investigated by Hide and Moroz [Hide, R. and Moroz, I.M., Effects due to induced azimuthal eddy currents in the self-exciting Faraday disk homopolar dynamo with a nonlinear series motor: I two special cases. Physica D 1999, 134, 387-301]. We extract unstable periodic orbits from long time series of chaotic trajectories by the method of close returns to a Poincaré section. We then employ recently developed topological tools to characterise the underlying chaotic attractor of the dynamo by identifying its branched manifold or template.