AppDynSys : Bifurcation Examples : Cusp Unfolding

This surface represent the equilibria in a 2-parameter family of 1-d systems modeled by the previous spring-disc system. Depending on the parameters, you can see saddle-nodes or hysteresis behaviors. At just the right values, you find a perfect (supercritical) pitchfork bifurcation.
(The vertical direction is the state: the two horizontal directions are parameters. In the 20th century, this was sensationally called a "cusp catastrophe" -- but that terminology was disastrous...)

[magicmike]

Pretty cool to see like this. First time I was exposed to bifurcation diagrams was in a mathematical biology course