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Stochastic calculus: application to dynamic bifurcations and threshold crossings

Kalvis M. Jansons·G. D. Lythe
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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.

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BibTeXRIS

Kalvis M. Jansons, G. D. Lythe. 1997-07-16. Stochastic calculus: application to dynamic bifurcations and threshold crossings. https://doi.org/10.1023/a%3A1023207919293

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