Intralayer and interlayer synchronization in multiplex network with higher-order interactions

TL;DR

This paper explores how higher-order interactions modeled by hypergraphs in multiplex networks enhance intralayer synchronization and improve the robustness of interlayer synchronization compared to pairwise interactions.

Contribution

It introduces a framework for analyzing synchronization in multiplex hypergraphs and derives conditions for stable synchronization states using the master stability function.

Findings

Higher-order interactions improve intralayer synchronization.

Interlayer synchronization is more robust in hypergraph-based multiplex networks.

Derived stability conditions match numerical simulations.

Abstract

Recent developments in complex systems have witnessed that many real-world scenarios, successfully represented as networks are not always restricted to binary interactions but often include higher-order interactions among the nodes. These beyond pairwise interactions are preferably modeled by hypergraphs, where hyperedges represent higher-order interactions between a set of nodes. In this work, we consider a multiplex network where the intralayer connections are represented by hypergraphs, called multiplex hypergraph. The hypergraph is constructed by mapping the maximal cliques of a scale-free network to hyperedges of suitable sizes. We investigate the intralayer and interlayer synchronization of such multiplex structures. Our study unveils that the intralayer synchronization appreciably enhances when the higher-order structure is taken into consideration inspite of only pairwise connections. We derive the necessary condition for stable synchronization states by the master stability function approach, which perfectly agrees with the numerical results. We also explore the robustness of interlayer synchronization and find that for the multiplex structures with many-body interaction, the interlayer synchronization is more persistent than multiplex networks with pairwise interaction.