Global synchronization in generalized multilayer higher-order networks

TL;DR

This paper develops a comprehensive framework to analyze global synchronization in multilayer networks with higher-order interactions, extending beyond pairwise connections and demonstrating enhanced synchronization stability through theoretical and simulation results.

Contribution

It introduces a novel framework for studying synchronization in multilayer higher-order networks, considering interactions beyond pairwise and across layers, with stability conditions similar to the master stability function.

Findings

Stable global synchronous state exists under certain conditions.

Higher-order interactions facilitate synchronization more effectively.

Simulations confirm theoretical predictions with neuronal and oscillator models.

Abstract

Networks incorporating higher-order interactions are increasingly recognized for their ability to introduce novel dynamics into various processes, including synchronization. Previous studies on synchronization within multilayer networks have often been limited to specific models, such as the Kuramoto model, or have focused solely on higher-order interactions within individual layers. Here, we present a comprehensive framework for investigating synchronization, particularly global synchronization, in multilayer networks with higher-order interactions. Our framework considers interactions beyond pairwise connections, both within and across layers. We demonstrate the existence of a stable global synchronous state, with a condition resembling the master stability function, contingent on the choice of coupling functions. Our theoretical findings are supported by simulations using Hindmarsh-Rose neuronal and R\"{o}ssler oscillators. These simulations illustrate how synchronization is facilitated by higher-order interactions, both within and across layers, highlighting the advantages over scenarios involving interactions within single layers.