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Scaling in directed dynamical small-world networks with random responses

Chen-Ping Zhu·Shi-Jie Xiong·Ying-Jie Tian·Lan Li·Ke-Sheng Jiang
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Abstract

A dynamical model of small-world network, with directed links which describe various correlations in social and natural phenomena, is presented. Random responses of every site to the imput message are introduced to simulate real systems. The interplay of these ingredients results in collective dynamical evolution of a spin-like variable S(t) of the whole network. In the present model, global average spreading length \langel L >_s and average spreading time _s are found to scale as p^-αln N with different exponents. Meanwhile, S behaves in a duple scaling form for N>>N^*: S ~ f(p^-βq^γt'_sc), where p and q are rewiring and external parameters, α, β, γand f(t'_sc) are scaling exponents and universal functions, respectively. Possible applications of the model are discussed.

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Chen-Ping Zhu, Shi-Jie Xiong, Ying-Jie Tian, Lan Li, Ke-Sheng Jiang. 2003-12-07. Scaling in directed dynamical small-world networks with random responses. https://doi.org/10.1103/physrevlett.92.218702

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