Synchronization onset for contrarians with higher-order interactions in multilayer systems

We investigate the impact of contrarians (via negative coupling) in multilayer networks of phase oscillators having higher-order interactions. We report that the multilayer framework facilitates synchronization onset in the negative pairwise coupling regime. The multilayering strength governs the onset of synchronization and the nature of the phase transition, whereas the higher-order interactions dictate the backward critical coupling. Specifically, the system does not synchronize below a critical value of the multilayering strength. The analytical calculations using the mean-field Ott-Antonsen approach agree with the simulations. The results presented here may be useful for understanding emergent behaviors in real-world complex systems with contrarians and higher-order interactions, such as the brain and social system.