SCALING OF MESSAGE DIFFUSION IN DIRECTED DYNAMICAL SMALL-WORLD NETWORKS WITH RANDOM RESPONSES

摘要

A dynamical model of small-world network (SWN), with directed links which describe a sort of correlations in social, economic and natural phenomena, is presented. Spatial disorder is introduced to yield random responses to input messages in sites of the network, which results in collective dynamical evolution of a spin-like variable S(t) of the whole network. In such dynamically varied SWNs, average spreading length < L >_s and average spreading time < T >_s are found to scale in p~(-α)lnN with indices 0.14 and 0.29, respectively. Meanwhile, isoparametic time t(S) behaves in another scaling law, t ～ p~(-β)f(S), where f(S) is a universal function and β = 0.23 ± 0.005 for N N~*. Possible applications of the model in different fields are discussed.