Volume 110, Number 6, June 2015
|Number of page(s)||4|
|Section||Condensed Matter: Structural, Mechanical and Thermal Properties|
|Published online||30 June 2015|
Synchronization in scale-free networks: The role of finite-size effects
1 Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR)- Physics Department, Universidad Nacional de Mar del Plata-CONICET - Funes 3350, (7600) Mar del Plata, Argentina
2 Center for Polymer Studies, Boston University - Boston, MA 02215, USA
Received: 5 May 2015
Accepted: 11 June 2015
Synchronization problems in complex networks are very often studied by researchers due to their many applications to various fields such as neurobiology, e-commerce and completion of tasks. In particular, scale-free networks with degree distribution , are widely used in research since they are ubiquitous in Nature and other real systems. In this paper we focus on the surface relaxation growth model in scale-free networks with , and study the scaling behavior of the fluctuations, in the steady state, with the system size N. We find a novel behavior of the fluctuations characterized by a crossover between two regimes at a value of that depends on λ: a logarithmic regime, found in previous research, and a constant regime. We propose a function that describes this crossover, which is in very good agreement with the simulations. We also find that, for a system size above , the fluctuations decrease with λ, which means that the synchronization of the system improves as λ increases. We explain this crossover analyzing the role of the network's heterogeneity produced by the system size N and the exponent of the degree distribution.
PACS: 68.35.Ct – Interface structure and roughness / 05.45.Xt – Synchronization; coupled oscillators / 89.75.Da – Systems obeying scaling laws
© EPLA, 2015
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