Scaling in directed dynamical small-world networks with random responses

Details Scaling in directed dynamical small-world networks with random responses Scaling in directed dynamical small-world networks with random responses

2003-12-07

arxiv.org/abs/cond-mat/0312179v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, 6 Figures

Scientific paper

10.1103/PhysRevLett.92.218702

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^-\alpha ln N with different exponents. Meanwhile, S behaves in a duple scaling form for N>>N^*: S ~ f(p^-\beta q^\gamma t'_sc), where p and q are rewiring and external parameters, \alpha, \beta, \gamma and f(t'_sc) are scaling exponents and universal functions, respectively. Possible applications of the model are discussed.

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