Synchronization in Scale Free networks: The role of finite size effects

TORRES. D; DI MURO. M. A; LA ROCCA. C. E; BRAUNSTEIN. L. A

EUROPHYSICS LETTERS

EPL ASSOCIATION

Lugar: Bologna; Año: 2015 vol. 110 p. 66001 - 66001

0295-5075

Synchronization problems in complex networks are very often studied by researchersdue to its many applications to various fields such as neurobiology, e-commerce and completion oftasks. In particular, Scale Free networks with degree distribution P(k) ∼ k−λ, are widely used inresearch since they are ubiquitous in nature and other real systems. In this paper we focus on thesurface relaxation growth model in Scale Free networks with 2.5 < λ < 3, and study the scalingbehavior of the fluctuations, in the steady state, with the system size N. We find a novel behaviorof the fluctuations characterized by a crossover between two regimes at a value of N = N∗thatdepends on λ: a logarithmic regime, found in previous research, and a constant regime. We proposea function that describes this crossover, which is in very good agreement with the simulations. Wealso find that, for a system size above N∗, the fluctuations decrease with λ, which means that thesynchronization of the system improves as λ increases. We explain this crossover analyzing therole of the network?s heterogeneity produced by the system size N and the exponent of the degreedistribution.