A microscopic spiking neuronal network for the age-structured model

TL;DR

This paper presents a microscopic spiking neuronal network model aligned with an age-structured equation, demonstrating well-posedness, propagation of chaos, and convergence rates, advancing the understanding of neural dynamics with delays.

Contribution

It introduces a novel microscopic spiking network model consistent with an existing age-structured PDE, including rigorous analysis of well-posedness and convergence properties.

Findings

Proves well-posedness of the particle system and mean-field equation

Establishes propagation of chaos for the network model

Quantifies convergence rate under exponential moment assumptions

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.