Up: Bifurcation

One-Dimensional Dynamical Systems

Part 5: Bifurcation

Qualitative change of dynamics

The theorem of Hartman and Grobman gives us the relationship between the slope of the graph at a fixed point and whether this fixed point is attracting, repelling, or neutral. For the Logistic map, we have already seen that the fixed point other than 0 is attracting for lambda = 1.5, because the slope is between -1 and 1. However, it is repelling for lambda = 3.1, since the graph of the derivative map no longer has a slope between -1 and 1. Hence, as we increase lambda, the fixed point changes from being attracting to being repelling. This scenario is called a bifurcation.

Up: Bifurcation

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Written by Hinke Osinga
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Created: Apr 6 1998 --- Last modified: Thu Apr 9 14:18:16 1998