ar X iv : m at h - ph / 9 90 80 23 v 1 2 5 A ug 1 99 9 Singularity theory study of overdetermination in models for L – H transitions

Two dynamical models that have been proposed for determining aspects of confined plasma behavior around L–H transitions are analysed using singular-ity theory and stability theory. The recognition problem for the unperturbed bifurcation sets is solved by applying singularity theory methods to determine the normal form and codimension of the singular points. We find that in both cases the unperturbed models are overdetermined bifurcation problems, and show how universal unfoldings improve the relationship between the mathematical models and the dynamical systems they represent. The question is addressed of whether and to what extent the bifurcation structures of the models indicate mutual equivalence.