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)

REFERENCES:

Rasband, S. N. Chaotic Dynamics of Nonlinear Systems. New York: Wiley, pp. 27-30, 1990.