Synchronization in Scale Free networks with degree correlation

TL;DR

This study investigates how degree-degree correlations in scale-free networks influence synchronization, revealing an optimal correlation for minimal load fluctuations and scalability, with potential technological implications.

Contribution

It extends previous work by analyzing the impact of degree correlations on synchronization and load fluctuations in scale-free networks.

Findings

Existence of an optimal correlation for synchronization.

Near optimal correlation, fluctuations are system size independent.

Far from optimal, fluctuations scale logarithmically with system size.

Abstract

In this paper we study a model of synchronization process on scale free networks with degree-degree correlations. This model was already studied on this kind of networks without correlations by Pastore y Piontti {\it et al.}, Phys. Rev. E {\bf 76}, 046117 (2007). Here, we study the effects of the degree-degree correlation on the behavior of the load fluctuations $W_s$ in the steady state. We found that for assortative networks there exist a specific correlation where the system is optimal synchronized. In addition, we found that close to this optimally value the fluctuations does not depend on the system size and therefore the system becomes fully scalable. This result could be very important for some technological applications. On the other hand, far from the optimal correlation, $W_s$ scales logarithmically with the system size.