A Fokker-Planck formalism for diffusion with finite increments and absorbing boundaries

Details A Fokker-Planck formalism for diffusion with finite increments and absorbing boundaries A Fokker-Planck formalism for diffusion with finite increments and absorbing boundaries

2009-08-13

arxiv.org/abs/0908.1960v3

Biology

Quantitative Biology

Quantitative Methods

Consists of two parts: main article (3 figures) plus supplementary text (3 extra figures)

Scientific paper

10.1371/journal.pcbi.1000929

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.

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