Instability of the homopolar disk-dynamo in presence of white noise
Résumé
We study a modified Bullard dynamo and show that this system is equivalent to a nonlinear oscillator subject to a multiplicative noise. The stability analysis of this oscillator is performed. Two bifurcations are identified, first towards an \lq\lq intermittent\rq\rq state where the absorbing (non-dynamo) state is no more stable but the most probable value of the amplitude of the oscillator is still zero and secondly towards a \lq\lq turbulent\rq\rq (dynamo) state where it is possible to define unambiguously a (non-zero) most probable value around which the amplitude of the oscillator fluctuates. The bifurcation diagram of this system exhibits three regions which are analytically characterized.