Hyperedge overlap modulates synchronization transitions in higher-order Sakaguchi-Kuramoto model

Synchronization phenomena in higher-order coupled systems have been widely studied, but the synergistic effect of microstructure and phase lag on synchronization has not been revealed. In this paper, we introduce the hyperedge overlap to quantify the degree of overlap between 2-hyperedges and analyze the hypergraph structures with the phase lag. The results show that increasing the phase lag and the hyperedge overlap drives the synchronization phase transition from first order to second order. Meanwhile, these changes decrease the global synchronization level, and this effect is independent of the network size. Under weak global synchronization, the smaller hyperedge overlap is associated with improved local synchronization performance. Furthermore, the phase lag changes the effective frequency distribution of the system, and the larger the coupling strength deviates more from the initial average frequency.