Robustness of truncated alpha-Omega dynamos with a dynamic alpha

In a recent work (Covas et al. 1997), the behaviour and the robustness of truncated $\alpha\Omega$ dynamos with a dynamic $\alpha$ were studied with respect to a number of changes in the driving term of the dynamic $\alpha$ equation, which was considered previously by Schmalz and Stix (1991) to be of the form $\sim A_{\phi}B_{\phi}$. Here we review and extend our previous work and consider the effect of adding a quadratic quenching term of the form $\alpha|B|^2$. We find that, as before, such a change can have significant effects on the dynamics of the related truncated systems. We also find intervals of (negative) dynamo numbers, in the system considered by Schmalz and Stix (1991), for which there is sensitivity with respect to small changes in the dynamo number and the initial conditions, similar to what was found in our previous work. This latter behaviour may be of importance in producing the intermittent type of behaviour observed in the sun.
Comment: Figures included. Also in http://www.maths.qmw.ac.uk/~eoc