Supercritical pitchfork bifurcation ($\dot{x}=\mu x-x^3$)

In the displayed pitchfork bifurcation normal form, zero is stable for $\mu <0$ and unstable for $\mu >0$. At $\mu =0$, a symmetric stable pair $x=\pm \sqrt{\mu }$ appears on the side where zero is unstable. Reversing the parameter orientation changes the side, while retaining the supercritical relationship between the new stable branches and the destabilized central branch.