xk+1 = f(xk ) = R xk
(1 - xk )
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.
Controls: Drag the blue curve by mouse to change R value.
Press <Enter> to set new parameters from the text fields.
You see iterations of f oN(x) = f(f(...f(x)))
for N = 2 below
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
Chaotic region zoom of the map
You can test that the map is chaotic for R < 0 too.
Previous: Transition to chaos through intermittency
Next: "Swallows" and "shrimps"
updated 8 Nov 06