Moderate Higher-Order Interactions Enhance Stability While Preserving Basin Structure

Abstract: Synchronization is a ubiquitous phenomenon in complex systems. The Kuramoto model serves as a paradigmatic framework for understanding how coupled oscillators achieve collective rhythm. Conventional approaches focus on pairwise interactions, but real-world systems frequently involve higher-order couplings among multiple elements. Previous studies have shown that higher-order interactions enrich dynamics but generally shrink the attraction basin of synchronized states, making synchronization harder to achieve. Here, we demonstrate this picture is incomplete. Through systematic analysis of twisted states on ring networks, we identify a moderate coupling regime where higher-order interactions enhance stability without altering basin structure. The relative distribution among twisted states remains constant, yet quasipotential barriers deepen as coupling strengths increase. By measuring mean first passage times, we show both pairwise and higher-order couplings contribute synergistically to enhance stability, consistent with large deviation theory. These findings provide new insights into the role of higher-order interactions in synchronization.