A discrete time neural network model with spiking neurons: II: dynamics with noise.

Journal of Mathematical Biology
B Cessac

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.

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Citations

Apr 19, 2011·Journal of Computational Neuroscience·Jonathan D Touboul, Olivier D Faugeras
Nov 26, 2011·Journal of Physiology, Paris·J C VasquezB Cessac
Mar 19, 2013·Journal of Physiology, Paris·B Cessac, R Cofré
Dec 19, 2014·Frontiers in Computational Neuroscience·Fereshteh Lagzi, Stefan Rotter
Nov 8, 2016·Scientific Reports·Ludmila BrochiniOsame Kinouchi
Jun 2, 2020·Frontiers in Neuroscience·Ahana GangopadhyayShantanu Chakrabartty
Sep 19, 2017·Frontiers in Neuroinformatics·Bruno CessacThierry Viéville
May 16, 2020·Frontiers in Neuroscience·Ying FangFeng Chen
Jan 10, 2021·Journal of Mathematical Neuroscience·Selma Souihel, Bruno Cessac
Dec 4, 2020·Entropy·Rodrigo CofréBruno Cessac
Oct 30, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·R Cofré, B Cessac

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