KURAMOTO MODEL
Mean-field synchronization: dφᵢ/dt = ωᵢ + (K/N)Σⱼ sin(φⱼ−φᵢ)
PARAMETERS
r = 0.00 | K_c = 0.00
Oscillators N:
80
Coupling K:
1.00
Freq spread σ:
1.0
Reset
Sweep K →
Pause
Transition at K_c = 2/πg(0):
For Lorentzian freq dist with width γ, K_c=2γ. Below K_c, incoherent; above, r grows as r~√(1−K_c/K).
Discovered by Kuramoto (1975) — a mean-field model of biological clocks, power grids, neural oscillators.