appears in nonlinear dynamics of biological population. By change of variable it is reduced to the quadratic family. As since logistic maps are very popular, here you can see iteration and bifurcation diagram for this family.

You see iterations of *f ^{ oN}(x) = f(f(...f(x)))*
for

*Controls:* Click mouse to zoom in *2* times. Click mouse with
*Ctrl* to zoom out. Hold *Shift* key to zoom in the *R*
(vertical) direction only. Max number of iterations = 4000.
See coordinates of the image center and *Δx,
ΔR* in the text field. The vertical line goes through *x = 1/2*
(see Bifurcation diagram for quadratic maps for
more detailes).

Chaotic region zoom of the map

You can test that the map is chaotic for *R < 0* too.

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