Dynamic range of hypercubic stochastic excitable media.

We study the response properties of d-dimensional hypercubic excitable networks to a stochastic stimulus. Each site, modeled 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 and sensitivity of the response function are 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.