Synchronized chaos in coupled double disk homopolar dynamos

Symmetrically coupled systems of N self-exciting Faraday disk homopolar dynamos have been proposed by Hide [1997] as a testbed for both the analytical and numerical study of the dynamics of coupled dynamo systems. There arises a natural hierarchy of systems, consisting of a series of N single disk dynamos, each in series with a motor [Hide et al., 1996]. Synchronization in the dynamics of these systems is investigated. The transition from the special case of strict amplitude and linear phase locking to the case of more general synchronization is examined. The particular case of two magnetically coupled homopolar dynamos with dissimilar characteristics is considered; the behavior of this N = 2 case is governed by six-coupled nonlinear ordinary differential equations which contain a total of thirteen dimensionless parameters. It is proved that for sufficiently small perturbations, the states of each of the two component dynamos are locked together. Numerical results suggest that this lockingextends to finite perturbations, the state of one system being a linear function of the state of the other. As the size of the perturbation increases, this strict phase locking is lost, yet the complicated chaotic trajectories of each dynamo appear to remain strictly synchronized. This paper is therefore the result of a previous study of coupled dynamos [Moroz et al., 1998] in which no more than five of the parameters were assumed to be independent.