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

Bruno Cessac 1, *
* Corresponding author
1 NEUROMATHCOMP
CRISAM - Inria Sophia Antipolis - Méditerranée , INRIA Rocquencourt, ENS Paris - École normale supérieure - Paris, UNS - Université Nice Sophia Antipolis, CNRS - Centre National de la Recherche Scientifique : UMR8548
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.
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Bruno Cessac. Statistics of spike trains in conductance-based neural networks: Rigorous results. Journal of Mathematical Neuroscience, BioMed Central, 2011, 1 (1), pp.8. ⟨hal-00640501v2⟩

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