Kuramoto Mean-Field Synchronization

N oscillators with natural frequencies ωᵢ couple through the mean field: dθᵢ/dt = ωᵢ + K·r·sin(ψ−θᵢ). The order parameter r = |⟨eⁱθ⟩| measures synchrony. The critical coupling K_c = 2/πg(0) depends on the frequency distribution width — below K_c the incoherent state persists; above it, a synchronized cluster grows.

Parameters

K_c = 2.00
K/K_c = 1.00
Order r = 0.00
Mean ψ = 0.00°
Time = 0.00