Let
be a one-parameter family of map satisfying

(1) | |||

(2) | |||

(3) | |||

(4) | |||

(5) |

Then there are intervals having a single stable fixed point and three fixed points (two of which are stable and one of which is unstable). This Bifurcation is called a pitchfork bifurcation. An example of an equation displaying a pitchfork bifurcation is

(6) |

**References**

Guckenheimer, J. and Holmes, P. *Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, 3rd ed.*
New York: Springer-Verlag, pp. 145 and 149-150, 1997.

Rasband, S. N. *Chaotic Dynamics of Nonlinear Systems.* New York: Wiley, p. 31, 1990.

© 1996-9

1999-05-25