A microscopic spiking neuronal network for the age-structured model

Abstract

We introduce a microscopic spiking network consistent with the age-structured/renewal equation proposed by Pakdaman, Perthame and Salort. It is a jump process interacting through a global activity variable with random delays. We show the well-posedness of the particle system and the mean-field equation. Moreover we show the propagation of chaos property and we quantify the rate of convergence under the assumption of exponential moments on the initial data.