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

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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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Authors and Affiliations

  1. Equipe systèmes dynamiques, interactions en physique, biologie, chimie, Laboratoire Jean-Alexandre Dieudonné, Université de Nice, Parc Valrose, 06000, Nice, France

    B. Cessac

  2. NeuroMathComp, INRIA, 2004 Route des Lucioles, 06902, Sophia-Antipolis, France

    B. Cessac

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  1. B. Cessac
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Cessac, B. A discrete time neural network model with spiking neurons: II: Dynamics with noise. J. Math. Biol. 62, 863–900 (2011). https://doi.org/10.1007/s00285-010-0358-4

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  • DOI: https://doi.org/10.1007/s00285-010-0358-4

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