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arXiv · 0707.2947

Discrete surface growth process as a synchronization mechanism for scale free complex networks

A. L. Pastore y Piontti·P. A. Macri·L. A. Braunstein
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Abstract

We consider the discrete surface growth process with relaxation to the minimum [F. Family, J. Phys. A {\bf 19} L441, (1986).] as a possible synchronization mechanism on scale-free networks, characterized by a degree distribution $P(k) \sim k^{-λ}$, where $k$ is the degree of a node and $λ$ his broadness, and compare it with the usually applied Edward-Wilkinson process [S. F. Edwards and D. R. Wilkinson, Proc. R. Soc. London Ser. A {\bf 381},17 (1982) ]. In spite of both processes belong to the same universality class for Euclidean lattices, in this work we demonstrate that for scale-free networks with exponents $λ<3$ this is not true. Moreover, we show that for these ubiquitous cases the Edward-Wilkinson process enhances spontaneously the synchronization when the system size is increased, which is a non-physical result. Contrarily, the discrete surface growth process do not present this flaw and is applicable for every $λ$.

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A. L. Pastore y Piontti, P. A. Macri, L. A. Braunstein. 2007-09-28. Discrete surface growth process as a synchronization mechanism for scale free complex networks. https://doi.org/10.1103/physreve.76.046117

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