Stochastic calculus: application to dynamic bifurcations and threshold crossings

Details Stochastic calculus: application to dynamic bifurcations and threshold crossings Stochastic calculus: application to dynamic bifurcations and threshold crossings

1997-07-16

arxiv.org/abs/adap-org/9707003v1

J. Stat. Phys (1997)

Nonlinear Sciences

Adaptation and Self-Organizing Systems

LaTeX, 34 pages, 7 postscript figures included

Scientific paper

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.

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