Conservative model for synchronization problems in complex networks

TL;DR

This paper investigates the interface roughness scaling in conservative noise models on complex networks, finding that the steady-state roughness remains independent of system size across different network types, contrasting with non-conservative models.

Contribution

It demonstrates that in conservative noise models on scale-free networks, the steady-state roughness does not depend on system size, unlike non-conservative models, and shows non-linear terms are irrelevant for this behavior.

Findings

Steady-state roughness is size-independent on scale-free networks.

Contrasts with non-conservative noise models where roughness scales with system size.

Non-linear terms are not relevant in describing the scaling behavior for conservative noise.

Abstract

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 $W_s$.