Dynamics and spike trains statistics in conductance-based integrate-and-fire neural networks with chemical and electric synapses

2012/12/14 by Rodrigo Cofré, Bruno Cessac
Biochemistry, Genetics and Molecular Biology · Engineering · Mathematics · Neuroscience · Physics and Astronomy · #Advanced Memory and Neural Computing #Computer science #Neural dynamics and brain function #Physics #Spike (software development) #Spike train #Statistical physics #Train #math-ph #math.MP #physics.bio-ph #q-bio.NC #stochastic dynamics and bifurcation

paper · pdf · doi:10.1016/j.chaos.2012.12.006

42 pages, 1 figure, submitted

arxiv created 2012/12/14 · openalex publication_date 2013/01/30 · arxiv updated 2017/07/26 · openalex created_date 2019/07/30 · openalex updated_date 2026/07/23

Abstract

We investigate the effect of electric synapses (gap junctions) on collective neuronal dynamics and spike statistics in a conductance-based Integrate-and-Fire neural network, driven by a Brownian noise, where conductances depend upon spike history. We compute explicitly the time evolution operator and show that, given the spike-history of the network and the membrane potentials at a given time, the further dynamical evolution can be written in a closed form. We show that spike train statistics is described by a Gibbs distribution whose potential can be approximated with an explicit formula, when the noise is weak. This potential form encompasses existing models for spike trains statistics analysis such as maximum entropy models or Generalized Linear Models (GLM). We also discuss the different types of correlations: those induced by a shared stimulus and those induced by neurons interactions.

Citations

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