KURAMOTO SYNCHRONIZATION

N phase oscillators: dθᵢ/dt = ωᵢ + (K/N)Σ sin(θⱼ−θᵢ). Order parameter r = |Σ e^(iθⱼ)|/N measures coherence. Above the critical coupling K_c = 2/πg(0) (g = frequency distribution), synchronization emerges spontaneously.

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r = 0.000