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Mean-field limit of neural networks with dendritic componenta smoothly interacting through threshold hitting-times

We study an original model for the membrane potentials of a network of neurons which involves a general diffusion process, connection strengths, and the delay needed by a spike to transmit from a synapse along the dendritic tree to the soma. We shortly discuss some modelling issues. We then prove the convergence of a stochastic particle system that interacts through threshold hitting times towards a non classical equation of McKean-Vlasov type and we prove that the limit equation is well-posed. (This is a joint work with James Inglis, Inria).

CMAP UMR 7641 École Polytechnique CNRS, Route de Saclay, 91128 Palaiseau Cedex France, Tél: +33 1 69 33 46 23 Fax: +33 1 69 33 46 46