Rhythmic dynamics of higher-order phase oscillator populations with competitive couplings

Synchronization is a critical phenomenon that is essential for elucidating the collective behaviors in nature. Here, we investigate the rhythmic dynamics in a system of globally coupled phase oscillators incorporating the higher-order time-varying coupling, in which the two-body and three-body interactions are encoded with the competitive dynamics described by the Lotka-Volterra model. Remarkably, we uncover that the co-evolving coupling manifesting the competition between the pairwise and nonpairwise interactions can significantly shape the collective dynamics toward synchronization. In particular, we reveal that the subtle balance between the dyadic and triadic coupling trajectories in the reduced phase diagram is responsible for the emergence of involved macroscopic rhythmic dynamics. Our findings provide insights for comprehending the underlying mechanism for the occurrence of diverse rhythmic behaviors encountered in complex systems, in which the higher-order and time-varying couplings dominate the interactions.