Dynamic range of hypercubic stochastic excitable media

TL;DR

This study investigates how hypercubic excitable networks respond to stochastic stimuli across different dimensions, revealing that the maximum dynamic range occurs at phase transitions and decreases with increasing dimension.

Contribution

It provides a comprehensive analysis of the response properties of d-dimensional hypercubic excitable media using simulations and mean field approximations, highlighting the relation between phase transitions and dynamic range.

Findings

Maximum dynamic range occurs at the phase transition to self-sustained activity.

Dynamic range decreases as the dimension d increases.

Results are consistent across different models and approximation methods.

Abstract

We study the response properties of d-dimensional hypercubic excitable networks to a stochastic stimulus. Each site, modelled either by a three-state stochastic susceptible-infected-recovered-susceptible system or by the probabilistic Greenberg-Hastings cellular automaton, is continuously and independently stimulated by an external Poisson rate h. The response function (mean density of active sites rho versus h) is obtained via simulations (for d=1, 2, 3, 4) and mean field approximations at the single-site and pair levels (for all d). In any dimension, the dynamic range of the response function is maximized precisely at the nonequilibrium phase transition to self-sustained activity, in agreement with a reasoning recently proposed. Moreover, the maximum dynamic range attained at a given dimension d is a decreasing function of d.