Fluctuations of a surface relaxation model in interacting scale free networks

TL;DR

This paper investigates how the fluctuations in a surface relaxation model behave in two interacting scale-free networks, revealing that slight increases in inter-network dependency links significantly reduce fluctuations, especially at low dependency levels.

Contribution

It introduces a novel analysis of surface relaxation fluctuations in interacting scale-free networks, linking the behavior to dependency links and interface growth dynamics.

Findings

Fluctuations decrease significantly with small increases in dependency links.

Strong interactions lead to only slight fluctuation changes.

Dispersion depends on internal degree and the growth model's integer nature.

Abstract

Isolated complex networks have been studied deeply in the last decades due to the fact that many real systems can be modeled using these types of structures. However, it is well known that the behavior of a system not only depends on itself, but usually also depends on the dynamics of other structures. For this reason, interacting complex networks and the processes developed on them have been the focus of study of many researches in the last years. One of the most studied subjects in this type of structures is the Synchronization problem, which is important in a wide variety of processes in real systems. In this manuscript we study the synchronization of two interacting scale-free networks, in which each node has $ke$ dependency links with different nodes in the other network. We map the synchronization problem with an interface growth, by studying the fluctuations in the steady state of a scalar field defined in both networks. We find that as $ke$ slightly increases from $ke=0$, there is a really significant decreasing in the fluctuations of the system. However, this considerable improvement takes place mainly for small values of $ke$, when the interaction between networks becomes stronger there is only a slight change in the fluctuations. We characterize how the dispersion of the scalar field depends on the internal degree, and we show that a combination between the decreasing of this dispersion and the integer nature of our growth model are the responsible for the behavior of the fluctuations with $ke$.