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

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 the 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 synchronizations of such multiplex structures. Our study unveils that the intralayer synchronization appreciably enhances when a higher-order structure is taken into consideration in spite 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 the multiplex networks with solely pairwise interaction.

Global synchronization on time-varying higher-order structures

“…By considering the simultaneous interactions of many agents, higher-order structures, namely hypergraphs [19] and simplicial complexes [20], offer a more comprehensive understanding of complex systems. These higher-order structures have been proven to produce novel features in various dynamical processes, including consensus [21,22], random walks [23,24], pattern formation [14,25,26], synchronization [14,[27][28][29][30][31][32], social contagion and epidemics [33,34]. Nevertheless, the suggested framework is not sufficiently general to describe systems with many-body interactions that vary with time.…”

Synchronization in simplicial complexes of memristive Rulkov neurons

“…In contrast, as the asymmetry varied, synchronization was achievable. Multiplex higher-order network was the subject that Anwar and Ghosh ( 2022 ) pursued. They looked for synchronization in a two-layer network within each layer, the 500 Rössler oscillators interacting via diffusive pairwise and non-pairwise connections and structured in a scale-free configuration.…”

Stability of synchronization in simplicial complexes with multiple interaction layers

“…The neuronal system is an example where, on the one hand, individual neurons are connected via electrical and chemical synapses [54,61], and on the other hand, proof of many-body interactions between individual neurons have recently been found [7,[62][63][64]. Nevertheless, the interplay between higher-order structures and multilayer networks [65], under some aspects has yet to be investigated, and specifically, the study of synchronization is still in its early stages [66,67]. In the previous study [66] of synchronization on multilayer framework with higherorder interactions, the interactions between individual elements of a particular layer are considered to be of a specific functional form (linear diffusive).…”

“…Nevertheless, the interplay between higher-order structures and multilayer networks [65], under some aspects has yet to be investigated, and specifically, the study of synchronization is still in its early stages [66,67]. In the previous study [66] of synchronization on multilayer framework with higherorder interactions, the interactions between individual elements of a particular layer are considered to be of a specific functional form (linear diffusive). These linear interactions factorize the many-body structures into pairwise interactions due to the superposition property of linear functions, resulting in a weighted pairwise network.…”