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

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

1999-08-25

arxiv.org/abs/math-ph/9908023v3

Phys.Rev.Lett. 84 (2000) 3077

Physics

Mathematical Physics

Latex (Revtex) source + 13 small postscript figures. Revised version

Scientific paper

10.1103/PhysRevLett.84.3077

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.

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