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

TL;DR

This paper investigates the convergence of a stochastic particle system modeling neural networks with dendritic structures, leading to a new McKean-Vlasov type equation, with implications for understanding neural dynamics.

Contribution

It introduces a novel particle system interaction through threshold hitting times and derives its mean-field limit, connecting neural models with advanced stochastic analysis.

Findings

Proves convergence of the particle system to a McKean-Vlasov equation

Models neural networks with dendritic components more accurately

Provides mathematical framework for neural dynamics with threshold interactions

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.