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arXiv · 0707.0309

Dynamic range of hypercubic stochastic excitable media

Vladimir R. V. Assis·Mauro Copelli
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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.

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Vladimir R. V. Assis, Mauro Copelli. 2008-02-13. Dynamic range of hypercubic stochastic excitable media. https://doi.org/10.1103/physreve.77.011923

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