Published 2011
| Version v1
Journal article
A discrete time neural network model with spiking neurons II. Dynamics with noise
- Creators
- Cessac, Bruno
- Others:
- NEUROMATHCOMP ; Inria Sophia Antipolis - Méditerranée (CRISAM) ; Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-INRIA Rocquencourt ; Institut National de Recherche en Informatique et en Automatique (Inria)-École normale supérieure - Paris (ENS-PSL) ; Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université Nice Sophia Antipolis (1965 - 2019) (UNS) ; COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)
- ARC MACACC
Description
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.
Abstract
43 pages - Journal of Mathematical Biology, Volume 62, Issue 6 (2011), Page 863.
Abstract
International audience
Additional details
- URL
- https://hal.inria.fr/inria-00530115
- URN
- urn:oai:HAL:inria-00530115v1
- Origin repository
- UNICA