Kuramoto Mean-Field — Phase Locking Transition

N oscillators with natural frequencies ω_i drawn from a Lorentzian distribution couple via K/N·Σsin(θ_j−θ_i). Above a critical coupling K_c = 2/πg(0), a macroscopic synchronized cluster forms. The order parameter R = |Σe^{iθ}|/N jumps continuously from 0 — a mean-field phase transition in dynamical systems.

R = 0.00 | K_c = 2.00 | Phase: incoherent