Scaling laws and relaxation rate at first order desynchronization

Abstract

While divergences in correlation length and time, hallmarks of criticality, have been established for second-order transitions to synchronization in the Kuramoto model, a comprehensive understanding of analogous scalings for abrupt transitions to desynchronization remains elusive. Through simulations and analytical calculations, we investigate this discontinuous transition for the Kuramoto model with higher-order interactions. We report the emergence of critical slowing down, marked by a diverging relaxation time near the threshold. We verify a finite-time, finite-size scaling by applying the homogeneity assumption using system size, coupling strength, and time as relevant parameters. This work extends the theoretical foundations of critical scaling to include abrupt transitions in coupled oscillator systems. ©2026 American Physical Society.