Accepted:
December 2004
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/vol12/msid64/ | © Copyright 2008 | |||
| Volume 12 | Received: Accepted: |
November 2004 December 2004 |
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The case of the trapped singularities
Rowena Ball |
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| Abstract | |
| 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. | |
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Multimedia Links (none) Reference Links (none) Citation Reference Rowena Ball 2008, The case of the trapped singularities, Complexity International, Volume 12, Paper ID: msid64, URL: http://www.complexity.org.au/vol12/msid64/ |
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