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 , . Thus the folds satisfy , with . Between the folds there are three real equilibria, and outside them one. A transverse stable direction may be present in a higher-dimensional realization.
New to topics? Read the docs here!