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

TL;DR

This paper applies singularity and stability theory to analyze two models of L-H plasma confinement transitions, revealing their bifurcation structures and overdetermination issues, and providing universal unfoldings for understanding state transitions.

Contribution

It introduces a singularity theory approach to analyze L-H transition models, identifying their bifurcation types and overdetermination, which was not previously established.

Findings

Stationary-state bifurcation sets match standard normal forms.

Models are overdetermined bifurcation problems.

Universal unfoldings for the models are derived.

Abstract

Two dynamical models that have been proposed to describe transitions between low and high confinement states (L-H transitions) in confined plasmas are analysed using singularity theory and stability theory. It is shown that the stationary-state bifurcation sets have qualitative properties identical to standard normal forms for the pitchfork and transcritical bifurcations. The analysis yields the codimension of the highest-order singularities, from which we find that the unperturbed systems are overdetermined bifurcation problems and derive appropriate universal unfoldings. Questions of mutual equivalence and the character of the state transitions are addressed.