Hopf bifurcation normal form — synchronization onset
Order parameter R: — | Phase: —
Stuart-Landau: żᵢ = (μ − |zᵢ|²)zᵢ + iωᵢzᵢ + K/N·Σzⱼ — the normal form of any Hopf bifurcation. Natural frequencies ωᵢ drawn from Lorentzian distribution. Critical coupling K_c = 2/π·g(0) where g(0) is the peak of the frequency distribution. Left: oscillator phases on unit circle. Right: order parameter R(t) showing the synchronization transition.