Mean-field limit of a stochastic particle system smoothly interacting through threshold hitting-times and applications to neural networks with dendritic component

James Inglis 1, 2 Denis Talay 1
1 TOSCA - TO Simulate and CAlibrate stochastic models
CRISAM - Inria Sophia Antipolis - Méditerranée , IECL - Institut Élie Cartan de Lorraine : UMR7502
2 NEUROMATHCOMP - Mathematical and Computational Neuroscience
CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR6621
Abstract : In this article we study the convergence of a stochastic particle system that interacts through threshold hitting times towards a novel equation of McKean-Vlasov type. The particle system is motivated by an original model for the behavior of a network of neurons, in which a classical noisy integrate-and-fire model is coupled with a cable equation to describe the dendritic structure of each neuron.
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SIAM Journal on Mathematical Analysis, Society for Industrial and Applied Mathematics, 2015, 47 (5), pp.32. 〈https://doi.org/10.1137/140989042〉. 〈10.1137/140989042〉
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James Inglis, Denis Talay. Mean-field limit of a stochastic particle system smoothly interacting through threshold hitting-times and applications to neural networks with dendritic component. SIAM Journal on Mathematical Analysis, Society for Industrial and Applied Mathematics, 2015, 47 (5), pp.32. 〈https://doi.org/10.1137/140989042〉. 〈10.1137/140989042〉. 〈hal-01069398v4〉

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