Volume 90, Numbers 1-2, 227-251, DOI: 10.1023/A:1023207919293

Stochastic Calculus: Application to Dynamic Bifurcations and Threshold Crossings

Kalvis M. Jansons and 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 isin and the rate of change of the parameter mgr. 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.

Noise - stochastic calculus - applied probability - dynamic bifurcation - pitchfork bifurcation - neuron dynamics - excursions - local time - threshold crossing

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