| the fold | | the cusp | | the swallowtail | | the butterfly | | the hyperbolic umbilic | | the elliptic umbilic | | the parabolic umbilic | |

V = x^{3}

V_{(a)} = x^{3} - ax

The fold catastrophe properties will be studied by means of this applet

Stability of state variable equilibrium may be tested by clicking on a potential curve point.

The control space is one-dimensional; bifurcation set is made of only one point. The fold catastrophe is similar as the "all or none" law; its bifurcation set is the all or none threshold.

| the fold | | the cusp | | the swallowtail | | the butterfly | | the hyperbolic umbilic | | the elliptic umbilic | | the parabolic umbilic | |