Hopf Bifurcation — Stuart-Landau

Stuart-Landau: ż = (μ + iω)z − |z|²z. Below μ=0: stable fixed point. Above μ=0: supercritical Hopf — limit cycle of radius √μ. Watch trajectories spiral in or out as μ changes. Compare to subcritical Hopf (unstable limit cycle inside stable one).

Supercritical Hopf | μ=0.20 | Limit cycle radius: √μ ≈ 0.447