Stochastic stability of a system of perfect integrate-and-fire inhibitory neurons

TL;DR

This paper investigates the stochastic stability of a system of inhibitory neurons modeled as perfect integrate-and-fire processes, demonstrating convergence to a stable distribution through fluid approximation methods.

Contribution

It introduces a novel analysis of inhibitory neuron systems using stochastic process theory and proves convergence to stability with a fluid approximation approach.

Findings

Convergence to a stable distribution in total variation.

Modeling of neuron interactions as stochastic processes.

Application of fluid approximation to neural systems.

Abstract

We study a system of perfect integrate-and-fire inhibitory neurons. It is a system of stochastic processes which interact through receiving an instantaneous increase at the moments they reach certain thresholds. In the absence of interactions, these processes behave as a spectrally positive L\'evy processes. Using the fluid approximation approach, we prove convergence to a stable distribution in total variation.