Stochastic calculus: application to dynamic bifurcations and threshold crossings
adap-org
2015-06-24 v1 Adaptation and Self-Organizing Systems
q-bio
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.
Cite
@article{arxiv.adap-org/9707003,
title = {Stochastic calculus: application to dynamic bifurcations and threshold crossings},
author = {Kalvis M. Jansons and G. D. Lythe},
journal= {arXiv preprint arXiv:adap-org/9707003},
year = {2015}
}
Comments
LaTeX, 34 pages, 7 postscript figures included