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 μ. 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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Jansons, K.M., Lythe, G.D. Stochastic Calculus: Application to Dynamic Bifurcations and Threshold Crossings. Journal of Statistical Physics 90, 227–251 (1998). https://doi.org/10.1023/A:1023207919293
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DOI: https://doi.org/10.1023/A:1023207919293