Hey @Zoe Erickson, Here’s a simple way to turn your loops into a proper bifurcation (orbit) diagram for the logistic map
Key idea: for each value of the parameter r, iterate the logistic map many times, discard a “transient” of iterations, and plot the remaining values of P against that r.
I am attaching the code below for referecne, modify it accordingly:
close all
clear
figure
hold on
% Parameter sweep for r
r_values = linspace(3,4,1000);
% Number of total iterations per r
num_iters = 300;
% Number of last points to plot (after transient)
num_plot = 100;
% Initial condition(s)
P0 = 0.5;
for r = r_values
% Preallocate
P = zeros(1,num_iters);
P(1) = P0;
% Iterate logistic map
for n = 1:num_iters-1
P(n+1) = r * P(n) * (1 - P(n));
end
% Plot only the last num_plot points (to avoid transients)
idx = (num_iters - num_plot + 1):num_iters;
plot(r * ones(1,num_plot), P(idx), '.k', 'MarkerSize', 1);
end
xlabel('r')
ylabel('Population P_n')
title('Bifurcation Diagram of the Logistic Map')
axis([3 4 0 1])
box on
hold off
