Kuramoto Synchrony

Coupled oscillators self-organizing into phase lock

Order parameter R = — | K_c ≈ —

The Kuramoto model: dθᵢ/dt = ωᵢ + (K/N)Σⱼ sin(θⱼ−θᵢ). The critical coupling K_c = 2/πg(0) where g is the frequency distribution. Below K_c oscillators spin incoherently; above K_c a macroscopic cluster locks. The order parameter R = |⟨e^{iθ}⟩| measures coherence.