Stochastic calculus: application to dynamic bifurcations and threshold crossings

Abstract

For the dynamic pitchfork bifurcation in the presence of white noise, the statistics of the last time at zero are calculated as a function of the noise level and the rate of change of the parameter. The threshold crossing problem used, for example, to model the firing of a single cortical neuron is considered, concentrating on quantities that may be experimentally measurable but have so far received little attention. Expressions for the statistics of pre-threshold excursions, occupation density and last crossing time of zero are compared with results from numerical generation of paths.

LaTeX, 34 pages, 7 postscript figures included

References in corpus (2)

• Domain formation in transitions with noise and time-dependent bifurcation parameter
• Noise and slow-fast dynamics in a three-wave resonance problem

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