AppDynSys : Bifurcations : 2-D Saddle-Node

Why is the "saddle-node bifurcation" called that? Because in 2-D, this bifurcation has two equilibria colliding and annihilating. The two equilibria are either a saddle and a sink or a saddle and a source. An old-fashioned term -- node -- is used for sources/sinks. Hence the name. Illustrated here are two parallel saddle-node bifurcations, one of each subtype.