Bifurcation diagram for discrete system using matlab code

Muhammad Anas

2020 7 18

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The following plot I want to plot. I used the following code but the result is almost similar but I want to join the points as it is in the below picture. Please some one help me to plot this following picture.

The model is

x(n+1)=(a*x(n)+b*y(n)*exp(-y(n)))*exp(-x(n))

y(n+1)=x(n)

Initial conditions are x(1)=2.512424567, y(1)=2.512424567 and a=0.5 where bifurcation parameter b varies in [10,250]

Figure 1 (Correct one)

Figure 2 (My result which I want same as figure 1)

figure(1);clf(1);
global a;
a=0.5;
clear z;z=zeros(100,2); z(1,1)=2.512424567;z(1,2)=2.512424567;
Max=25; step=10; interval=Max*step;
for n=1:Max
    b=step*n;
    for k=1:1000
        z(k+1,2)=(a*z(k,1)+b*z(k,2)*exp(-z(k,2)))*exp(-z(k,1));
        z(k+1,2)=z(k,1);
    end
    plot(b*ones(500),z(501:1000,1),'ko-'); xlabel('b');ylabel('x(n)');
    hold on
    z(1,1)=2.512424567;z(1,2)=2.512424567
end