Three-body interactions unveil devil's staircase, multistability, and synchronization revival in phase oscillators

Synchronization in systems with higher-order interactions remains a frontier in understanding collective behavior beyond pairwise coupling. This study investigates a minimal model of three nonidentical phase oscillators governed by pure three-body interactions, isolating the effects of three-body coupling from traditional pairwise terms. Key findings include the emergence of a complete devil's staircase in rotation numbers, structured by an anomalous Farey sequence, which arises from mutual coupling rather than external driving. The system exhibits robust multistability, where synchronous states coexist with phase-locked or quasi-periodic regimes, and basin stability of attractors is uncorrelated with their linear stability. Arnold tongues governing frequency-locking transitions display nonmonotonic broadening and bending, contrasting classical circle map predictions, and preventing chaotic dynamics. Notably, synchronous states revive at weak coupling strengths due to parameter-dependent reorganization of nullcline structures in the reduced phase-difference subsystem. These results highlight the intrinsic complexity of pure multibody interactions and provide insights into synchronization control in neural, social, and engineered systems. Our work establishes a foundational framework for studying minimal higher-order motifs and their role in collective dynamics.