Kuramoto Model — Finite-N Phase Oscillators

N phase oscillators with natural frequencies drawn from a Lorentzian distribution, coupled all-to-all: dθᵢ/dt = ωᵢ + (K/N)Σⱼ sin(θⱼ−θᵢ). Above K_c = 2/πg(0), spontaneous synchronization emerges. Finite-N fluctuations create irregular order parameter dynamics.

Parameters

N oscillators 50 Coupling K 2.0 Width γ (Lorentzian) 1.0 dt 0.05

r = 0.00
ψ = 0.00
t = 0.0
K_c = 0.00