Egwald Mathematics: Nonlinear Dynamics:

Interactive Logistic Map Diagrams

by

Elmer G. Wiens

The Logistic Map

The logistic interative map with parameter r is:

xt+1 = f(xt, r) = r * xt * (1 + xt),   x0 = x0 >= 0.       

The second order map f2 is given by:

xt+2  =  f(xt+1, r)  =  f (f(xt, r), r )

The third order map f3 is given by:

xt+3  = f( f (f(xt, r), r), r).

Repeat this sequence for the 4th, 5th, etc. order maps.

The value of the parameter r = 2 in the following phase diagram and solution trajectory diagram.

One can change the value of r (1 <= r <= 4), and the solution trajectory diagram's start time, td (0 <= td <= 600) in the form below.

r = 2     x1 = 0,   x2 = 0.5

Value of
parameter r:

Order n of
map fn:

Order m of
map fm:

Start trajectory
td value

         

Use the form above to set the value of r for the logistic map graphs along with the nth and mth order maps for 2 <= n, m <= 9. Set n = m if you want the logistic map and just one other map.

 

  
   

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