Universal scaling and phase transitions of coupled phase oscillator populations

Abstract

The Kuramoto model, which serves as a paradigm for investigating synchronization phenomenon of oscillatory system, is known to exhibit second-order, i.e., continuous, phase transitions in the macroscopic order parameter. Here, we generalize a number of classical results by presenting a general framework for capturing, analytically, the critical scaling of the order parameter at the onset of synchronization. Using a self-consistent approach and constructing a characteristic function, we identify various phase transitions toward synchrony and establish scaling relations describing the asymptotic dependence of the order parameter on coupling strength near the critical point. We find that the geometric properties of the characteristic function, which depends on the natural frequency distribution, determines the scaling properties of order parameter above the criticality.

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Cited by in corpus (4)

• Collective dynamics of heterogeneously and nonlinearly coupled phase oscillators
• Synchronization in the Kuramoto model in presence of stochastic resetting
• Generic criterion for explosive synchronization in heterogeneous phase oscillator populations
• Unified Ott--Antonsen Framework for Stability and Bifurcations in Ring Swarmalators