Dynamics of Axisymmetric Truncated Dynamo Models

Abstract

An important question regarding the study of mean field dynamo models is how to make precise the nature of their underlying dynamics. This is difficult both because relatively little is known about the dynamical behaviour of infinite dimensional systems and also due to the numerical cost of studying the related partial differential equations. As a first step towards their understanding, it is useful to consider the corresponding truncated models. Here we summarise some recent results of the study of a class of truncated axisymmetric mean field dynamo models. We find conclusive evidence in these models for various types of intermittency as well as multiple attractors and final state sensitivity. We also find that the understanding of the underlying dynamics of such dynamo models requires the study of a new class of dynamical systems, referred to as the {\it non-normal} systems. Current work demonstrates that these types of systems are capable of a novel type of intermittency and also of relevance for the understanding of the full axisymmetric PDE dynamo models.