Subcritical bifurcation

A subcritical branch emerges on the parameter side where the original state remains stable. In the cubic Landau amplitude equation $\dot{A}=\mu A-g|A{|}^{2}A$ with $g<0$, the small nonzero branch lies at $\mu <0$ and is unstable to radial amplitude perturbations. Higher-order saturation can generate a finite-amplitude stable branch and hysteresis, but this does not follow from a cubic truncation alone.