Deterministic Chaos

6.D.4. Bifurcation Diagram

s=0.7
s=1.5
s=2.0
s=2.5
s=3.1
s=3.5
s=3.6
s=3.826
s=3.85
s=3.9
s=4.0

The logistic map and the tent map are really families of functions: both depend on a parameter s. For each s, we get a different function. The values of the iterates of a point certainly can depend on s, and the bifurcation diagram is a method of organizing this data.
Specifically, the bifurcation diagram is a graph of the s-values on the horizontal axis, and above each s-value the iterates of some value, plotted vertically.
To emphasize the long-range behavior, sometimes the points are plotted only after a number of transients are computed but not plotted.
Selecting the s-values on the left, we see the bifurcation diagram for s up to that value, together with the graphical iteration plot and histogram at that s-value.

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