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We study the effects of network topology on the response of networks ofcoupled discrete excitable systems to an external stochastic stimulus. Weextend recent results that characterize the response in terms of spectralproperties of the adjacency matrix by allowing distributions in thetransmission delays and in the number of refractory states, and by developing anonperturbative approximation to the steady state network response. We confirmour theoretical results with numerical simulations. We find that the steadystate response amplitude is inversely proportional to the duration ofrefractoriness, which reduces the maximum attainable dynamic range. We alsofind that transmission delays alter the time required to reach steady state.Importantly, neither delays nor refractoriness impact the general predictionthat criticality and maximum dynamic range occur when the largest eigenvalue ofthe adjacency matrix is unity.

Effects of network topology, transmission delays, and refractoriness on the response of coupled excitable systems to a stochastic stimulus