Singularity theory study of overdetermination in models for L-H transitions

Two dynamical models that have been proposed to describe transitions betwee n low- and high-confinement states in confined plasmas are analyzed using s ingularity theory and stability theory. It is shown that the stationary-sta te bifurcation sets have qualitative properties identical to standard norma l forms for the pitchfork and transcritical bifurcations. The analysis yiel ds the codimension of the highest-order singularities, from which we find t hat the unperturbed systems are overdetermined bifurcation problems and der ive appropriate universal unfoldings. Questions of mutual equivalence and t he character of the state transitions are addressed.