STRUCTURAL STABILITY OF AXISYMMETRICAL DYNAMO MODELS

We examine the stability of the dynamical behaviour of axisymmetric alpha(2) omega dynamo models in rotating spherical shells as well as in spheres. Overall, our results show that the spherical dynamo models are more stable in the following senses: spherical models (i) do not seem to allow chaotic behaviour and (ii) are robust with respect to changes in the functional form of alpha. On the other hand, spherical shell models (i) are capable of producing chaotic behaviour for certain ranges of parameter values and (ii) possess, in the combined ''space'' of parameters and boundary conditions, regions of complicated behaviours, in the sense that there are regimes in which small changes in either the dynamo parameters or the boundary conditions can drastically change the qualitative behaviour of the model. Finally, we discuss briefly the physical relevance of our results.