Bifurcation Diagram of Logistic Equation -- Unnecessary Lines in Code?

clear all, close all,clc

xvals=[];

for beta =0:0.01:4
    beta
    xold = 0.5;
    for i = 1:2000
        xnew = ((xold-xold^2)*beta);
        xold = xnew;
    end
    xss = xnew;
    for i = 1:1000;
        xnew = ((xold-xold^2)*beta);
        xold = xnew;
        xvals(1,length(xvals)+1) = beta;
        xvals(2,length(xvals)) = xnew;
        if (abs(xnew-xss) < .001)
            break
        end
    end
end 
plot (xvals(1,:),xvals(2,:),'.')
        

Hello again,

I was following a youtube tutorial by Steve Brunton, (link:https://www.youtube.com/watch?v=_BvAkyuWhOI&t=395s),to create the bifurcation diagram of the logistic map, and I don' seem to understand what the purpose of this block of code is:

    for i = 1:2000
        xnew = ((xold-xold^2)*beta);
        xold = xnew;
    end

The next for loop I understand, but the one I quoted above does not make sense to me. Also, for the last loop (i = 1:1000), how/why did the length of the array change (we had to add one to the length) ?

Thank you in advance and thank you for your patience, as I am fairly new to numerical programming

Answer 1

[Guru Mohanty]

After debugging your code, it seems the section of code you mentioned is irreverent, because of following reasons.

for i = 1:2000
    xnew = ((xold-xold^2)*beta);
    xold = xnew
end

1. Inside the for loop there is no expressions depending on the index ‘i’. So the execution of above two line will continue 2000 times.
2. Each time the loop executes, the value of ‘xnew’ and ‘xold’ keep on decreasing and after the for-loop execution value of ‘xnew’ and ‘xold’ becomes Zero.

It would be helpful to run the code in Debug Mode.

[Maria Raheb]

Both for loops in the code do not depend on the index "i" though, so what makes that block of code different? Are you suggesting that that block of code be deleted from script?