Extensive multistability and scalings in coupled phase oscillators with pairwise or non-pairwise interactions

The paradigm of higher-order interactions has received considerable attention in recent years. Previous studies have reported that coupled phase oscillator systems exhibit extensive multistability and abrupt desynchronization transitions in the presence of non-pairwise interactions. This study advances current understanding by systematically comparing three distinct coupling strategies. The findings reveal that the addition of a higher (second) coupling mode and adaptive coupling enables the emergence of these complex macroscopic behaviors in systems with pairwise coupling. A theoretical framework is developed to elucidate the dynamic origins of these states. In particular, the mechanisms underlying multistability are clarified, the causes of irreversible abrupt desynchronization transitions are identified, and the critical scaling relationships between the Kuramoto and Daido order parameters and coupling strength are explored.