  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.
