1202.3053 (Cristian E. La Rocca et al.)

Conservative model for synchronization problems in complex networks    [PDF]

Cristian E. La Rocca, Lidia A. Braunstein, Pablo A. Macri

In this paper we study the scaling behavior of the interface fluctuations
(roughness) for a discrete model with conservative noise on complex networks.
Conservative noise is a noise which has no external flux of deposition on the
surface and the whole process is due to the diffusion. It was found that in
Euclidean lattices the roughness of the steady state $W_s$ does not depend on
the system size. Here, we find that for Scale-Free networks of $N$ nodes,
characterized by a degree distribution $P(k)\sim k^{-\lambda}$, $W_s$ is
independent of $N$ for any $\lambda$. This behavior is very different than the
one found by Pastore y Piontti {\it et. al} [Phys. Rev. E {\bf 76}, 046117
(2007)] for a discrete model with non-conservative noise, that implies an
external flux, where $W_s \sim \ln N$ for $\lambda < 3$, and was explained by
non-linear terms in the analytical evolution equation for the interface [La
Rocca {\it et. al}, Phys. Rev. E {\bf 77}, 046120 (2008)]. In this work we show
that in this processes with conservative noise the non-linear terms are not
relevant to describe the scaling behavior of $W_s$.

View original: http://arxiv.org/abs/1202.3053