Analysis and Computation of a Mean-Field Dynamo Model

We consider a mean-field dynamo where the α-effect and β-effect interact. The inclusion of the β term introduces a hyperbolicity into the model. We present a phase plane analysis for two scalar fields in a model of a galactic dynamo. Unlike a modal analysis, the specific boundary conditions are not crucial to most of our analysis. However, we consider only special initial conditions, and these are of dipole or quadrupole symmetry