Equilibrium loses stability and a limit cycle is born at μ = 0
μ = -0.50
Stable fixed point (μ < 0)
Supercritical Hopf: ṙ = μr − r³, θ̇ = ω. For μ < 0: stable fixed point. At μ = 0: bifurcation. For μ > 0: unstable fixed point + stable limit cycle of radius r* = √μ. The imaginary part of the eigenvalue (ω) determines oscillation frequency.