Multiple synchronization transitions in simplicial complexes on 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.

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).…”