Logistic maps

Logistic maps
    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.

Iteration diagram

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

Bifurcation diagram

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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updated 8 Nov 06