2004/10/20 by R. Ball, Rowena Ball, Ball, R.
Mathematics · Physics and Astronomy · #Adaptation and Self-Organizing Systems (nlin.AO) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Laser-Plasma Interactions and Diagnostics #Magnetic confinement fusion research #Plasma Physics (physics.plasm-ph) #Quantum chaos and dynamical systems #math.DS #nlin.AO #physics.plasm-ph
paper · pdf · doi:10.48550/arxiv.physics/0410160
21 pages, 12 figures, 34 postscript figure files
arxiv created 2004/10/20 · openalex publication_date 2004/10/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A case study in bifurcation and stability analysis is presented, in which reduced dynamical system modelling yields substantial new global and predictive information about the behaviour of a complex system. The first smooth pathway, free of pathological and persistent degenerate singularities, is surveyed through the parameter space of a nonlinear dynamical model for a gradient-driven, turbulence-shear flow energetics in magnetized fusion plasmas. Along the route various obstacles and features are identified and treated appropriately. An organizing centre of low codimension is shown to be robust, several trapped singularities are found and released, and domains of hysteresis, threefold stable equilibria, and limit cycles are mapped. Characterization of this rich dynamical landscape achieves unification of previous disparate models for plasma confinement transitions, supplies valuable intelligence on the big issue of shear flow suppression of turbulence, and suggests targeted experimental design, control and optimization strategies.