Onset of synchronization in contrarians with higher-order interactions

We investigate the impact of contrarians (via negative coupling) in a multilayer network of phase oscillators having higher-order interactions. We show 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 backward critical couplings depend on higher-order interaction strength. The system does not synchronize below a critical value of multilayering strength. The numerical results agree with the analytical predictions using the Ott-Antonsen approach. 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 society.