A walk in the parameter space of L-H transitions without stepping on or through the cracks

A mathematically and physically sound three-degree-of-freedom dynamical model that emulates low- to high-confinement mode (L--H) transitions is elicited from a singularity theory critique of earlier fragile models. We construct a smooth map of the parameter space that is consistent both with the requirements of singularity theory and with the physics of the process. The model is found to contain two codimension 2 organizing centers and two Hopf bifurcations, which underlie dynamical behavior that has been observed around L-H transitions but not mirrored in previous models. The smooth traversal of parameter space provided by this analysis gives qualitative guidelines for controlling access to H-mode and oscillatory regimes.