## Fold Bifurcation

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).