Mean-Field Limit of a Stochastic Particle System Smoothly Interacting Through Threshold Hitting-Times and Applications to Neural Networks with Dendritic Component

In this article, we study the convergence of a stochastic particle system that interacts through threshold hitting times toward 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.