[bs] Logistic map

Referensi : wikipedia

An example is the bifurcation diagram of the logistic map:

x(n+1) =  r*x(n)*(1-x(n))

The bifurcation parameter r is shown on the horizontal axis of the plot and the vertical axis shows the possible long-term population values of the logistic function.

The bifurcation diagram nicely shows the forking of the possible periods of stable orbits from 1 to 2 to 4 to 8 etc. Each of these bifurcation points is a period-doubling bifurcation. The ratio of the lengths of successive intervals between values of r for which bifurcation occursconverges to the first Feigenbaum constant.

Code matlab kita untuk logistic map sbb :

clc

clear all

r = 2.5:5e-4:4;

x = 0.4*ones(1,length(r));

k1 = 400;                   

k2 = 100;                   

f = zeros(k1+k2,length(r));

for i = 1:k1+k2

    x = r .* x .* (1 - x);

    f(i,:) = x;

end

f = f(k1+1:end,:);

figure(1)

plot(r,f,'b.','MarkerSize',1)

axis equal

xlabel('r','FontSize',16)

ylabel('x','FontSize',16);

Informasi sebelumnya mengenai chaotic map