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Statistics of spike trains in conductance-based neural networks: Rigorous results

Bruno Cessac

Author Affiliations

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

The Journal of Mathematical Neuroscience 2011, 1:8  doi:10.1186/2190-8567-1-8

Published: 25 August 2011

Abstract

We consider a conductance-based neural network inspired by the generalized Integrate and Fire model introduced by Rudolph and Destexhe in 1996. We show the existence and uniqueness of a unique Gibbs distribution characterizing spike train statistics. The corresponding Gibbs potential is explicitly computed. These results hold in the presence of a time-dependent stimulus and apply therefore to non-stationary dynamics.