Conservative model for synchronization problems in complex networks

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 $W_s$.