Assortative mixing enhances the irreversible nature of explosive synchronization in growing scale-free networks

TL;DR

This paper investigates how degree-degree correlations in scale-free networks influence explosive synchronization, revealing that moderate assortative mixing significantly enhances the irreversibility of the synchronization transition.

Contribution

It demonstrates that moderate assortative mixing in scale-free networks amplifies the hysteresis and irreversibility of explosive synchronization transitions.

Findings

Moderate assortative mixing maximizes hysteresis width.

High positive or negative mixing induces second-order transitions.

Assortative mixing characteristic of social networks enhances irreversibility.

Abstract

We discuss the behavior of large ensembles of phase oscillators networking via scale-free topologies in the presence of a positive correlation between the oscillators' natural frequencies and network's degrees. In particular, we show that the further presence of degree-degree correlation in the network structure has important consequences on the nature of the phase transition characterizing the passage from the phase-incoherent to the phase-coherent network's state. While high levels of positive and negative mixing consistently induce a second-order phase transition, moderate values of assortative mixing, such as those ubiquitously characterizing social networks in the real world, greatly enhance the irreversible nature of explosive synchronization in growing scale-free networks. This latter effect corresponds to a maximization of the area and of the width of the hysteretic loop that differentiates the forward and backward transitions to synchronization.