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

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 $\lambda$.

8 pages, 4 figures

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Cited by in corpus (11)

• Epidemic Model with Isolation in Multilayer Networks
• Evolution equation for a model of surface relaxation in complex networks
• Conservative model for synchronization problems in complex networks
• Interacting social processes on interconnected networks
• Synchronization in Scale Free networks with degree correlation
• Jamming in complex networks with degree correlation
• Competition between surface relaxation and ballistic deposition models in scale free networks
• A mechanism to synchronize fluctuations in scale free networks using growth models
• Synchronization in interacting Scale Free Networks
• Relevance of the minimum degree to dynamic fluctuation in strongly heterogeneous networks
• Fluctuations of a surface relaxation model in interacting scale free networks