Crisis-induced intermittency in truncated mean field dynamos

Abstract

We investigate the detailed dynamics of a truncated $\alpha\omega$ dynamo model with a dynamic $\alpha$ effect. We find the presence of multiple attractors, including two chaotic attractors with a fractal basin boundary which merge to form a single attractor as the control parameter is increased. By considering phase portraits and the scaling of averaged times of transitions between the two attractors, we demonstrate that this merging is accompanied by a crisis-induced intermittency. We also find a range of parameter values over which the system has a fractal parameter dependence for fixed initial conditions. This is the first time this type of intermittency has been observed in a dynamo model and it could be of potential importance in accounting for some forms of intermittency in the solar and stellar output.