Kuramoto Model — Synchronization
N coupled phase oscillators · collective order parameter R
Parameters
Oscillators N:
50
Coupling K:
2.0
Freq. spread σ:
1.0
Order Parameter R(t)
0.00
Phase coherence 0→1
Reset / Resample
Pause
Kuramoto (1975):
dθᵢ/dt = ωᵢ + (K/N)Σⱼ sin(θⱼ−θᵢ)
Order parameter: R·e
iψ
= (1/N)Σ e
iθⱼ
Critical coupling: K_c = 2σ√(π/2)
Above K_c, oscillators lock and R→1.