A Fokker-Planck formalism for diffusion with finite increments and absorbing boundaries
Abstract
Gaussian white noise is frequently used to model fluctuations in physical systems. In Fokker-Planck theory, this leads to a vanishing probability density near the absorbing boundary of threshold models. Here we derive the boundary condition for the stationary density of a first-order stochastic differential equation for additive finite-grained Poisson noise and show that the response properties of threshold units are qualitatively altered. Applied to the integrate-and-fire neuron model, the response turns out to be instantaneous rather than exhibiting low-pass characteristics, highly non-linear, and asymmetric for excitation and inhibition. The novel mechanism is exhibited on the network level and is a generic property of pulse-coupled systems of threshold units.
Keywords
Cite
@article{arxiv.0908.1960,
title = {A Fokker-Planck formalism for diffusion with finite increments and absorbing boundaries},
author = {M. Helias and M. Deger and S. Rotter and M. Diesmann},
journal= {arXiv preprint arXiv:0908.1960},
year = {2010}
}
Comments
Consists of two parts: main article (3 figures) plus supplementary text (3 extra figures)