Coupling strength driven synchronization optimization in higher-order networks

Higher-order interactions are ubiquitous in real-world systems and can fundamentally alter collective dynamical behaviors. Yet, how network topology governs synchronizability when higher-order interactions exist remains poorly understood. In this work, we address this problem by studying synchronization regulation in hypergraph networks with simultaneous pairwise and many-body couplings. Our results show that the optimal synchronizability of networks can be strongly regulated by the ratio of higher- to low-order coupling strengths. Specifically, the synchronization-optimal network undergoes a structured transition from a low-order dominated homogeneous topology to a higher-order dominated homogeneous topology, with an intermediate regime characterized by strong disassortative coordination between interaction orders, i.e., synchronizability exhibits a non-monotonic dependence on the coupling strength ratio. Effective measures of global homogeneity and hybrid assortativity are introduced to explain these findings. The proposed coupling strength-driven framework for synchronization regulation in higher-order networks provides theoretical guidance for the design of synchronization-optimal systems with many-body interactions.