bifurcation for Fractional order

I need an example matlab code to draw a bifurcation diagram for a fractional orde system. (for parametre varying or FO q varying, as seen in figures)

I've done some research on the subject and found The code by @Marius-F. Danca (2023) can be found at this File Exchange link:

Matlab code for FO logistic map, MATLAB Central File Exchange. Retrieved October 24, 2023.

However, I can't plot the bifurcation diagram for the FO case.

code for the graphical representation of the bifurcation proposed by Sam Chak

interval  = [2.8 4.0];
accuracy  = 0.001;
reps      = 100;     % number of repetitions
numtoplot = 50;
initidx   = reps - (numtoplot - 1);

for r  = interval(1):accuracy:interval(2)
    x  = 0.4;
    xo = x;
    for n  = 2:reps
        xn = r*xo*(1 - xo);
        x  = [x xn];
        xo = xn;
    end
    plot(r*ones(numtoplot), x(initidx:reps), '.', 'MarkerSize', 1, 'Color', '#be4d25'),
    hold on
end

hold off
xlim([2.8 4])
title('Logistic Map')
xlabel('\itr', 'FontSize', 14)
ylabel('\itx', 'FontSize', 14)

However, the fractional order need a workaround, i fond the code by @Marius-F. Danca

but I don't know how it works, Can anyone kindly share *.m file

function [u]=FO_discrete(q,p,u0,n_max)
% Author: Marius-F. Danca 2021
    u=zeros(n_max,1); % memory alocation
    u(1)=u0+f(u0); % u(1) outside of the loops 
    for n=2:n_max; % $u(2),u(3),...,n(n_max)$
        s=exp(gammaln(n-1+q)-gammaln(n))*f(u0); 
        for j=2:n;
            s=s+exp(gammaln(n-j+q)-gammaln(n-j+1))*f(u(j-1));
        end
        u(n)=u0+s/gamma(q);
    end
    function ff=f(x); % logistic map
    ff=p*x*(1-x);
    end
end

[Sam Chak]

Hi @Ali Abl

I've already advised you to post the code for plotting the bifurcation diagram. This would enable others to examine the code directly and troubleshoot it without having to search for various types of Fractional-Order Bifurcation Maps. If you have some free time, please edit your post to insert the two codes by clicking this icon , as previously advised.

[Ali Abl]

@Sam Chak Done

[Vedat Ertürk]

Hello Ali;

did you solve your problem?

[Ali Abl]

Hello,

unfortunately not yet

[haifeng]

hi,i have a pI have a possible solution code that can implement a fractional order bifurcation diagram of the Lorentz system, but due to copyright issues, it cannot be publicly shared. If you need it, please contact me by email and I will send it to you. [e-mail]