Synchronization in interacting Scale Free Networks

TL;DR

This paper investigates how interconnecting scale-free networks affects synchronization, showing that increased external links significantly reduce fluctuations and improve synchronization, largely independent of network degree distribution.

Contribution

It demonstrates that external interconnections enhance synchronization in scale-free networks by reducing fluctuations through diffusion, regardless of degree distribution.

Findings

Fluctuations decrease as the fraction of interconnections increases.

Synchronization improves by nearly 40% at full interconnection.

The effect is largely independent of the networks' degree distribution.

Abstract

We study the fluctuations of the interface, in the steady state, of the Surface Relaxation Model (SRM) in two scale free interacting networks where a fraction $q$ of nodes in both networks interact one to one through external connections. We find that as $q$ increases the fluctuations on both networks decrease and thus the synchronization reaches an improvement of nearly $40\%$ when $q=1$. The decrease of the fluctuations on both networks is due mainly to the diffusion through external connections which allows to reducing the load in nodes by sending their excess mostly to low-degree nodes, which we report have the lowest heights. This effect enhances the matching of the heights of low-and high-degree nodes as $q$ increases reducing the fluctuations. This effect is almost independent of the degree distribution of the networks which means that the interconnection governs the behavior of the process over its topology.