= Cusp bifurcation
{title2=$\dot x=\beta_1+\beta_2x-x^3$}
A cusp is a two-parameter degeneracy at which two <saddle-node bifurcation> curves meet and the reduced steady equation has a triple root. In the displayed scalar <normal form>, simultaneous vanishing of the polynomial and its derivative gives $\beta_2=3x^2$, $\beta_1=-2x^3$. Thus the folds satisfy $4\beta_2^3=27\beta_1^2$, with $\beta_2\geq0$. Between the folds there are three real <equilibria>, and outside them one. A transverse stable direction may be present in a higher-dimensional realization.
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