= Solution
A <Hopf bifurcation> occurs when a simple pair of <complex conjugate> <eigenvalues> crosses the imaginary axis at nonzero frequency. A supercritical <normal form of a dynamical system> is
$$
\boxed{\dot z=(\mu+i\omega_0)z-|z|^2z,\qquad\omega_0\ne0.}
$$
Writing $z=re^{i\theta}$ gives $\dot r=\mu r-r^3$ and $\dot\theta=\omega_0$. A stable <periodic orbit> of radius $\sqrt\mu$ is born for $\mu>0$ as the equilibrium loses stability. In contrast, a subcritical Hopf has an unstable small <periodic orbit> on the side where the equilibrium is still stable.
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