  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.
