Stability of synchronization under stochastic perturbations in leaky integrate and fire neural networks of finite size

TL;DR

This paper investigates how fully-connected, excitatory integrate-and-fire neural networks maintain synchronization despite stochastic noise, providing theoretical stability results and probability bounds for synchronization.

Contribution

It introduces a large deviation principle approach to prove the stability of synchronized states under stochastic perturbations and offers bounds on synchronization probability.

Findings

Synchronized states are stable under Gaussian white noise perturbations.

A lower bound on synchronization probability demonstrates robustness.

Synchronization can emerge and persist despite stochastic influences.

Abstract

We study the synchronization of fully-connected and totally excitatory integrate and fire neural networks in presence of Gaussian white noises. Using a large deviation principle, we prove the stability of the synchronized state under stochastic perturbations. Then, we give a lower bound on the probability of synchronization for networks which are not initially synchronized. This bound shows the robustness of the emergence of synchronization in presence of small stochastic perturbations.