A discrete time neural network model with spiking neurons II. Dynamics with noise
Dynamical Systems
2011-05-18 v3 Probability
Biological Physics
Neurons and Cognition
Abstract
We provide rigorous and exact results characterizing the statistics of spike trains in a network of leaky integrate and fire neurons, where time is discrete and where neurons are submitted to noise, without restriction on the synaptic weights. We show the existence and uniqueness of an invariant measure of Gibbs type and discuss its properties. We also discuss Markovian approximations and relate them to the approaches currently used in computational neuroscience to analyse experimental spike trains statistics.
Keywords
Cite
@article{arxiv.1002.3275,
title = {A discrete time neural network model with spiking neurons II. Dynamics with noise},
author = {B. Cessac},
journal= {arXiv preprint arXiv:1002.3275},
year = {2011}
}
Comments
43 pages - revised version - to appear il Journal of Mathematical Biology