Saddle-Node / Cusp Bifurcation

Normal form: ẋ = r + x². At r=0 a stable and unstable fixed point collide and annihilate. The cusp catastrophe adds a linear term a·x.

r (bifurcation param): 0.00 a (asymmetry): 0.00 View: Phase portrait Cusp surface Time series

Cusp: fold surface in (a,r) space. Hysteresis loops when crossing the cusp fold.