Let be a one-parameter family of map satisfying
then there exist intervals , and such that
1. If , then has two fixed points in with the positive one being unstable and the negative one stable, and
2. If , then has no fixed points in .
This type of bifurcation is known as a fold bifurcation, sometimes also called a saddle-node bifurcation or tangent bifurcation. An example of an equation displaying a fold bifurcation is
(Guckenheimer and Holmes 1997, p. 145).