Stochastic calculus: application to dynamic bifurcations and threshold crossings

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...

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Bibliographic Details
Published in:arXiv.org 1997-07
Main Authors: Jansons, Kalvis M, Lythe, G D
Format: Article
Language:English
Subjects:
Bifurcations
Mathematical models
White noise
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.9707003