When higher-order interactions enhance synchronization: the case of the Kuramoto model

Abstract: Synchronization is a fundamental phenomenon in complex systems, observed across a wide range of natural and engineered contexts. The Kuramoto model provides a foundational framework for understanding synchronization among coupled oscillators, traditionally assuming pairwise interactions. However, many real-world systems exhibit group and many-body interactions, which can be effectively modeled through hypergraphs. Previous studies suggest that higher-order interactions shrink the attraction basin of the synchronous state, making it harder to reach and potentially impairing synchronization, despite enriching the dynamics. In this work, we show that this is not always the case. Through extensive numerical analysis of the higher-order Kuramoto model, we find that while strong higher-order interactions do generally work against synchronization, weak higher-order interactions can actually enhance it. This result is further corroborated by a cost-benefit analysis: under a constrained budget of both pairwise and higher-order interactions, a mixed allocation involving both consistently achieves higher synchronization than relying on either interaction type alone. These findings provide new insights into the role of higher-order interactions in shaping collective dynamics and point to design principles for optimizing synchronization in complex systems.