ON A CODIMENSION-3 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 recentl y derived model for self-exciting dynamo action introduced by Hide et al. [R. Hide, A.C. Skeldon, D.J. Acheson, A study of two novel self-ex citing single-disk homopolar dynamos: theory, Proc. R. Sec. Lend. A 45 2 (1996) 1369-1395]. The general unfolding of such a codimension-three bifurcation has already been discussed in an abstract setting by Li a nd Rousseau [Codimension-2 symmetric homoclinic bifurcations and appli cation to 1:2 resonance, Can J. Math. 42 (1990) 191-212]. Here we desc ribe the unfolding scenario in the context of the dynamo problem. In p articular we compare the behaviour predicted by the normal form analys is with a bifurcation study of the full dynamo equations in the neighb ourhood of the codimension-three point. Copyright (C) 1998 Published b y Elsevier Science B.V.