Up: Bifurcation

One-Dimensional Dynamical Systems

Part 5: Bifurcation

Bifurcation points

The Logistic map has an attracting fixed point for lambda = 1.5 that becomes repelling as we increase lambda to 3.1.

Definition (Bifurcation): If the qualitative dynamics of f changes as the parameter lambda is varied, we call this a bifurcation.

Definition (Bifurcation Point): In case of a bifurcation, there is a special value lambdab for which the following holds: the dynamics for lambda close to but smaller than lambdab is qualitatively different from the dynamics for lambda close to but larger than lambdab This value lambdab is called a bifurcation point.

Not every value of lambda 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 lambda.

Up: Bifurcation

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Written by Hinke Osinga
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Created: Apr 6 1998 --- Last modified: Wed Apr 8 19:48:50 1998