Periodic and aperiodic behaviour in stellar dynamos

The authors have constructed a simple parametrized mean field dynamo model that includes the dynamical interaction between the magnetic field and differential rotation. This system of seven coupled nonlinear ordinary differential equations has finite amplitude oscillatory solutions (corresponding to Parker's dynamo waves) when the dynamo number D>1. Two regimes have been studied. In the first, the velocity shear is reduced by the Lorentz force and there are stable periodic solutions for all D>1. In the second there is a transition from strictly periodic oscillations to aperiodic (chaotic) behaviour as D is increased. This simple example shows that nonlinear hydromagnetic dynamos can produce aperiodic cycles, with Maunder minima, as observed in the Sun and other late-type stars. (Auth.)