Scaling in directed dynamical small-world networks with random responses

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 <T >_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.

4 pages, 6 Figures

References in corpus (16)

• Statistical mechanics of complex networks
• The large-scale organization of metabolic networks
• The spread of epidemic disease on networks
• Evolution of networks
• Epidemic dynamics and endemic states in complex networks
• Epidemics and percolation in small-world networks
• Fast Response and Temporal Coding on Coherent Oscillations in Small-World Networks
• Small world effect in an epidemiological model
• Robust Patterns in Food Web Structure
• Ising model in small-world networks
• Nonequilibrium Phase Transitions in Directed Small-World Networks
• Small-world networks and the conformation space of a lattice polymer chain
• Relaxation Properties of Small-World Networks
• Localization-Delocalization Transition of Electron States in a Disordered Quantum Small World Network
• Quantum and classical diffusion in small-world networks
• Simple models of small world networks with directed links

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