Fold catastrophe
Stable and unstable pair of extrema disappear at a fold bifurcation
At negative values of a, the potential has two extrema - one stable, and one unstable. If the parameter a is slowly increased, the system can follow the stable minimum point. But at a=0 the stable and unstable extrema meet, and annihilate. This is the bifurcation point. At a>0 there is no longer a stable solution. If a physical system is followed through a fold bifurcation, one therefore finds that as a reaches 0, the stability of the a<0 solution is suddenly lost, and the system will make a sudden transition to a new, very different behaviour. This bifurcation value of the parameter a is sometimes called the tipping point.
source- wikipedia
