On a Codimension Three Bifurcation Arising in a Simple Dynamo Model

In this paper we investigate the dynamics associated with a degenerate codimension two Takens-Bogdanov bifurcation which arises in a recently derived model for selfexciting dynamo action introduced by Hide et al. [1]. The general unfolding of such a codimension three bifurcation has already been discussed in an abstract setting by Li and Rousseau [4]. Here we describe the unfolding scenario in the context of the dynamo problem. In particular we compare the behaviour predicted by the normal form analysis with a bifurcation study of the full dynamo equations in the neighbourhood of the codimension three point.