One-Dimensional Dynamical Systems
Part 5: Bifurcation
The Logistic map has an attracting fixed point for
= 1.5 that
becomes repelling as we increase
Definition (Bifurcation): If the qualitative dynamics of f changes as the parameter is varied, we call this a bifurcation.
Definition (Bifurcation Point): In case of a bifurcation, there is a special value b for which the following holds: the dynamics for close to but smaller than b is qualitatively different from the dynamics for close to but larger than b This value b is called a bifurcation point.
Not every value of is a bifurcation point. Only when a qualitative change in the dynamics occurs, we say that the function underwent a bifurcation.
In the following section we show how to visualize the dynamics as a function of .
Written by Hinke Osinga
Comments to: firstname.lastname@example.org
Created: Apr 6 1998 --- Last modified: Wed Apr 8 19:48:50 1998