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One-Dimensional Dynamical Systems

Part 4: Linear and Nonlinear Behaviour

 In the first part of this course you investigated the eventual behaviour of the Logistic map. That is, you investigated the orbit of x0 for different choices of x0, and studied what happens as you vary lambda. In the second part of this course we take a more mathematical viewpoint and not only describe what happens, but also ask ourselves why this happens.

Linear versus nonlinear

The phenomenon where an attracting fixed point becomes repelling, and at the same time an attracting periodic orbit of period 2 appears, is called period-doubling. It is an example of a bifurcation.

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Copyright © 2001 by Hinke Osinga
Last modified: Thu Feb 1 18:44:55 2001