STRUCTURAL STABILITY OF AXISYMMETRICAL DYNAMO MODELS

We examine the stability of the dynamical behaviour of axisymmetric al pha(2) omega dynamo models in rotating spherical shells as well as in spheres. Overall, our results show that the spherical dynamo models ar e more stable in the following senses: spherical models (i) do not see m to allow chaotic behaviour and (ii) are robust with respect to chang es in the functional form of alpha. On the other hand, spherical shell models (i) are capable of producing chaotic behaviour for certain ran ges 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 chan ge the qualitative behaviour of the model. Finally, we discuss briefly the physical relevance of our results.