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

Abstract

We consider a conductance based neural network inspired by the generalized Integrate and Fire model introduced by Rudolph and Destexhe. 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 presence of a time-dependent stimulus and apply therefore to non-stationary dynamics.

42 pages, 1 figure, to appear in Journal of Mathematical Neuroscience

References in corpus (4)

• Mean Field Theory For Non-Equilibrium Network Reconstruction
• Spin glass models for a network of real neurons
• Entropy-based parametric estimation of spike train statistics
• Delayed feedback causes non-Markovian behavior of neuronal firing statistics