Effects of network topology, transmission delays, and refractoriness on the response of coupled excitable systems to a stochastic stimulus

TL;DR

This paper investigates how network topology, transmission delays, and refractoriness influence the response of coupled excitable systems to stochastic stimuli, providing theoretical insights and numerical validation.

Contribution

It extends spectral response analysis to include delay and refractory state distributions and develops a nonperturbative approximation for steady state response.

Findings

Steady state response amplitude decreases with longer refractoriness.

Transmission delays affect the time to reach steady state.

Criticality and maximum dynamic range occur at the largest eigenvalue of one.

Abstract

We study the effects of network topology on the response of networks of coupled discrete excitable systems to an external stochastic stimulus. We extend recent results that characterize the response in terms of spectral properties of the adjacency matrix by allowing distributions in the transmission delays and in the number of refractory states, and by developing a nonperturbative approximation to the steady state network response. We confirm our theoretical results with numerical simulations. We find that the steady state response amplitude is inversely proportional to the duration of refractoriness, which reduces the maximum attainable dynamic range. We also find that transmission delays alter the time required to reach steady state. Importantly, neither delays nor refractoriness impact the general prediction that criticality and maximum dynamic range occur when the largest eigenvalue of the adjacency matrix is unity.