Kuramoto model (1975): N oscillators each with natural frequency ωᵢ ~ N(0,σ²), coupled by
dθᵢ/dt = ωᵢ + (K/N)Σⱼ sin(θⱼ − θᵢ)
The order parameter r·e^{iψ} = (1/N)Σ e^{iθⱼ} measures synchrony: r≈0 incoherent, r≈1 locked.
Phase transition at Kc = 2σ/π. Above Kc, r grows as √(K−Kc). Below, r→0 (thermodynamic limit).