Effects due to induced Azimuthal Eddy currents in a Self-exciting Faraday Disk homopolar dynamo with a nonlinear Series Motor II: the General Case

This paper forms the second part of a two-part study into the effects of azimuthal eddy currents in the Faraday disk self-exciting homopolar dynamo, connected in series with the coil when the applied couple driving the disk is steady. The Lorentz couple driving the armature of the motor is a general quadratic function I(1 - e + eSI) of the current I(t), where 0 ≤ e ≤ 1. Here we investigate how cases with 0 < e < 1 relate to the two special cases of e = 0 and e = 1, considered in Part I of our study [Hide & Moroz, 1999]. One key difference is that the lack of reflectional symmetry in the general e problem means that the linear stability curves for the onset of both steady and oscillatory behavior for both the trivial and the nontrivial equilibrium solutions no longer coincide. This results in distinct Takens–Bogdanov double-zero bifurcations for these states, as well as multiple branches to the Hopf bifurcation curves, associated with bifurcations from the nontrivial equilibrium states. Multiple bifurcations involving simultaneous steady and nondegenerate oscillatory solutions are also possible.