Flip Bifurcation

Let be a one-parameter 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)