Image:Logistic-burification.png

Burification diagram of a logistic map

Generation scripts Here are some GNU Octave scripts to experiment with the generation of bifurcation diagrams for the logistic map.

 r_min = 2.5; r_max = 4; # the range of parameter values we study
 n = 1000; # the number of parameter values we consider in this range

 t_max = 1000; # how many iterations to simulate per parameter value
 p_max = 100; # the last p_max iterations are plotted

 x0 = 0.1; # we use the same initial value x0 for all parameters.

 r = linspace(r_min, r_max, n);
 pop = zeros(p_max, n);

 for k = 1:n
   x = population(r(k), x0, t_max);
   pop(:, k) = x(t_max-p_max+1:t_max);
 end

 gset nokey;
 plot(r, pop, 'b.');

 function x =  population(r, x0, n)
 # simulates n iterations of the logistic map with parameter
 # r and initial value x0. The results are returned in the
 # array x.
   x = zeros(n, 1);
   x(1) = x0;
   for k = 1:n-1
     x(k + 1) = r * x(k) * (1 - x(k));
   end

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