= Solution
A <saddle-node bifurcation> creates or destroys two equilibria when a real <eigenvalue> passes through zero with a nonzero quadratic normal-form term. With a <parameter> orientation chosen so the pair appears for $\mu>0$, use
$$
\boxed{\dot q=\mu-q^2.}
$$
There are no equilibria for $\mu<0$, a double nonhyperbolic equilibrium at zero, and equilibria $q=\pm\sqrt\mu$ for $\mu>0$. The positive branch is stable and the negative branch unstable in the active direction; additional hyperbolic directions can make them a node and a <saddle equilibrium>. “Supercritical” for a fold depends on this chosen <parameter> orientation; unlike the pitchfork and Hopf cases it is not an intrinsic distinction between the stability of two possible cubic branches.
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