Multiple synchronization transitions in simplicial complexes on multilayer networks

TL;DR

This paper reveals that simplicial complexes on multilayer networks can exhibit multiple synchronization transitions, with an analytical framework explaining the origins and stability of these complex dynamical states.

Contribution

It introduces a novel analytical approach to understand multiple synchronization transitions in simplicial complexes on multilayer networks.

Findings

Multiple basins of attraction lead to various routes to synchronization.

Analytical framework explains stability of different dynamical states.

Rich dynamical behaviors relevant to real-world multilayer networks.

Abstract

The presence of higher-order interactions (simplicial complexes) in networks and certain types of multilayer networks has shown to lead to the abrupt first-order transition to synchronization. We discover that simplicial complexes on multilayer networks can yield multiple basins of attraction, leading to multiple routes to the abrupt first-order transition to synchronization. Using the Ott-Antonsen approach, we develop an analytical framework for simplicial complexes on multilayer networks, which thoroughly explains the origin and stability of all possible dynamical states, including multiple synchronization transitions, of the associated coupled dynamics. The study illustrating rich dynamical behaviours could be pivotal to comprehending the impacts of higher-order interactions on dynamics of complex real-world networks, such as brain, social and technological, which have inherent multilayer networks architecture.