One-Dimensional Dynamical Systems
Part 5: Bifurcation
Bifurcation points
The Logistic map has an attracting fixed point for
= 1.5 that
becomes repelling as we increase
to 3.1.
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:
webmaster@geom.umn.edu
Created: Apr 6 1998 ---
Last modified: Wed Apr 8 19:48:50 1998