Mean field approximation for noisy delay coupled excitable neurons

TL;DR

This paper derives a mean field approximation for large networks of noisy, delay-coupled FitzHugh-Nagumo neurons, simplifying complex stochastic delay equations into two deterministic delay-differential equations with accurate stability and bifurcation predictions.

Contribution

It introduces a novel mean field approximation for noisy delay-coupled neurons that accurately predicts system dynamics with reduced complexity.

Findings

Excellent prediction of stability and bifurcations

Simplification from stochastic delay equations to deterministic equations

Effective modeling of large neural networks

Abstract

Mean field approximation of a large collection of FitzHugh-Nagumo excitable neurons with noise and all-to-all coupling with explicit time-delays, modelled by $N\gg 1$ stochastic delay-differential equations is derived. The resulting approximation contains only two deterministic delay-differential equations but provides excellent predictions concerning the stability and bifurcations of the averaged global variables of the exact large system.