Effect of small-world topology on wave propagation on networks of excitable elements

TL;DR

This paper investigates how small-world network topology influences wave propagation in networks of excitable elements, revealing the impact of coupling strength and long-range links on wave resilience and failure mechanisms.

Contribution

It introduces a reaction-diffusion approximation with mean-field correction to estimate critical long-range link density for propagation failure.

Findings

High coupling strength enhances wave resilience.

Long-range links can cause propagation failure.

Reaction-diffusion model accurately predicts critical link density.

Abstract

We study excitation waves on a Newman-Watts small-world network model of coupled excitable elements. Depending on the global coupling strength, we find differing resilience to the added long-range links and different mechanisms of propagation failure. For high coupling strengths, we show agreement between the network and a reaction-diffusion model with additional mean-field term. Employing this approximation, we are able to estimate the critical density of long-range links for propagation failure.