One-body theory for amplified signal response in a scale-free network

It has recently been shown that amplified signal response is possible in scale-free networks of two-state signaling devices [J. A. Acebron et al., Phys. Rev. Lett. 99, 128701 (2007)]. In the analysis of dynamics in networks, much emphasis is put on the hub, and consequently the applicability thereof is limited to a region of small coupling strength. In this paper, we develop a one-body theory which predicts (1) the behavior of the gain in the whole coupling strength region, and (2) the degree of the unit, which shows maximum response, as a function of the coupling strength. In order to achieve good agreement with numerical experiments effects of finite system size are taken into account when the coupling strength becomes very small and the degree k(L) of the maximum response unit, predicted by our theory, becomes larger than the maximum degree k(max) available to a concrete finite network.