• DOI:10.1103/PhysRevLett.84.3077
• Corpus ID: 3036974

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

@article{Ball1999SingularityTS,
  title={Singularity theory study of overdetermination in models for L-H transitions},
  author={Ball and Dewar},
  journal={Physical review letters},
  year={1999},
  volume={84 14},
  pages={
          3077-80
        }
}

• Ball, Dewar
• Published 25 August 1999
• Mathematics
• Physical review letters

Two dynamical models that have been proposed to describe transitions between low- and high-confinement states in confined plasmas are analyzed 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.