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

TL;DR

This paper compares two surface growth processes as synchronization mechanisms on scale-free networks, revealing that the discrete process is more reliable than the Edward-Wilkinson process for networks with degree exponent less than 3.

Contribution

It demonstrates that the discrete surface growth process remains effective for all degree exponents, unlike the Edward-Wilkinson process which fails for certain scale-free networks.

Findings

Discrete process works for all lambda values.

Edward-Wilkinson process enhances synchronization non-physically for lambda<3.

Discrete process avoids size-dependent divergence in synchronization.

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 $P(k) \sim k^{-\lambda}$, where $k$ is the degree of a node and $\lambda$ 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 $\lambda<3$ 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 $\lambda$.