Let be a oneparameter family of maps satisfying
(1)
 
(2)
 
(3)
 
(4)

Then there are intervals , , and such that
1. If , then has one unstable fixed point and one stable orbit of period two for , and
2. If , then has a single stable fixed point for .
This type of bifurcation is known as a flip bifurcation. An example of an equation displaying a flip bifurcation is
(5)
