On the role of higher-order interactions towards first synchronization time

Understanding how large complex networks achieve synchronization is a problem of fundamental interest, and is typically studied in the asymptotic steady-state regime. In contrast, this study investigates how higher-order interactions affect the time required to reach steady-state synchronization in a complex dynamical system. To this end, an analytical expression for the first synchronization time is derived using the Ott-Antonsen ansatz on a Kuramoto oscillator network with higher-order interactions. Subsequent numerics reveal that increasing coupling strengths accelerates the transition to synchronization, whereas increasing the interaction order produces non-monotonic behavior. In particular, the inclusion of triadic interactions accelerates synchronization, whereas further incorporating higher-order interactions progressively delays convergence to the steady state, in some regimes even falling below the pairwise case.