The orbit diagram for the logistic family

I can't seem to figure out what to do to make this code for the orbit diagram for the logistic family. I'm very new to MatLab, could someone help me out? This is what I have:

close all;
clear all;
hold on;
 
for r = linspace(3,4,1000)
    for P_initial = linspace(0.1, 0.9, 100)
        num_iters = 250;
        
        
        P(1) = P_initial;
        
        for n=1:(num_iters - 1)
            P(n + 1) = r*P(n)*(1 - P(n));
        end
        plot(r,P(num_iters),'.')
        axis([0,4,0,2]);
    end
end

Answer 1

[BhaTTa]

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

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