Cluster synchronization on sparse simplicial complexes with higher-order repulsive coupling

Abstract Higher-order interactions are widely existed in complex systems, which induce diverse phenomena beyond pairwise interactions. Here, we explore the nonlinear dynamics of higher-order Kuramoto model on sparse simplicial complexes. We observe anti-phase cluster synchronization, where individuals within a system spontaneously divide into two opposing groups, when both pairwise and three-body interactions are repulsive. We investigate the microscopic mechanisms behind this phenomenon and reveal that multiple edges shared by multiple 2-simplices facilitate its emergence. Furthermore, we explore the suppressing impact of pairwise-only interactions on this synchronization and explain the trade-off between multiple and pairwise-only edges underlying the system’s structure. Our findings are further validated on the heterogeneous simplicial complex and real dataset. Finally, we discuss the splitting of non-antiphase clusters under the traveling wave states when pairwise interactions become attractive. These results highlight the unique mechanism of repulsive coupling, offering valuable insights into the relationship between higher-order structures and dynamics, and contributing to a deeper understanding of synchronization in real-world systems, such as social networks and the brain.