Symmetries and synchronization in multilayer random networks

TL;DR

This paper explores how symmetries and asymmetries in interlayer connections of multilayer networks influence synchronization, revealing that asymmetries can enhance synchronization in complex oscillator systems.

Contribution

It demonstrates that asymmetries in interlayer connections promote synchronization, providing insights into the AISync mechanism in multilayer networks with complex oscillators.

Findings

Symmetries in interlayer connections reduce network synchronization.

Asymmetries in interlayer connections enhance synchronization.

Results applicable to understanding optimal network structures for synchronization.

Abstract

In the light of the recently proposed scenario of asymmetry-induced synchronization (AISync), in which dynamical uniformity and consensus in a distributed system would demand certain asymmetries in the underlying network, we investigate here the influence of some regularities in the interlayer connection patterns on the synchronization properties of multilayer random networks. More specifically, by considering a Stuart-Landau model of complex oscillators with random frequencies, we report for multilayer networks a dynamical behavior that could be also classified as a manifestation of AISync. We show, namely, that the presence of certain symmetries in the interlayer connection pattern tends to diminish the synchronization capability of the whole network or, in other words, asymmetries in the interlayer connections would enhance synchronization in such structured networks. Our results might help the understanding not only of the AISync mechanism itself, but also its possible role in the determination of the interlayer connection pattern of multilayer and other structured networks with optimal synchronization properties.