MATLAB: How to plot bifurcation with Delay Differential equations

Question

I want to draw the bifurcation diagram for the model.

All parameters are positve constant.

The value of parameters are as:

A1 = 0.8463, A2 = 0.6891, K = 1.2708, beta1 = 0.4110, beta2 = 0.1421,

The diagram are vary tau from 68 to 72 in steps of 0.001. For inital conditions X(0) = 0.26 and Y(0) = 0.58.

Please ansers me for Matlab code to plot the bifurcation diagrams.

Answer 1

How about the following for your loop (it assumed you have defined tau earlier in the file):

for j=1:N+1
    if t(j)<=tau
        xd = x(1); 
        yd = y(1);
    else
       d = ceil((t(j)-tau)/h);
       xd = x(d);
       yd = y(d);
    end
       
        
    t(j+1)=t(j)+h;
    %tempx(j+1)=tempx(j)+h;
    %tempy(j+1)=tempy(j)+h;
      
    k1x=fx(t(j),    x(j),   y(j));
    k1y=fy(t(j),    xd,   yd, y(j));
    %k1y=fy(t(j),    x(j),   y(j),   tempx(j),  tempy(j));
    k2x=fx(t(j)+h/2,    x(j)+h/2*k1x,   y(j)+h/2*k1y);
    k2y=fy(t(j)+h/2,    xd+h/2*k1x,   yd+h/2*k1y, y(j)+h/2*k1y);
    %k2y=fy(t(j)+h/2,    x(j)+h/2*k1x,   y(j)+h/2*k1y,  tempx(j)+h/2*k1x,    tempy(j)+h/2*k1y);
    
    k3x=fx(t(j)+h/2,    x(j)+h/2*k2x,   y(j)+h/2*k2y);
    k3y=fy(t(j)+h/2,    xd+h/2*k2x,   yd+h/2*k2y, y(j)+h/2*k2y); 
    %k3y=fy(t(j)+h/2,    x(j)+h/2*k2x,   y(j)+h/2*k2y,  tempx(j)+h/2*k2x,    tempy(j)+h/2*k2y);
    
    k4x=fx(t(j)+h,  x(j)+h*k3x, y(j)+h*k3y);
    k4y=fy(t(j)+h,  xd+h*k3x, yd+h*k3y, y(j)+h*k3y); 
    %k4y=fy(t(j)+h,  x(j)+h*k3x, y(j)+h*k3y,  tempx(j)+h*k3x,    tempy(j)+h*k3y);
    
    x(j+1)=x(j)+h/6*(k1x+2*k2x+2*k3x+k4x);
    y(j+1)=y(j)+h/6*(k1y+2*k2x+2*k3y+k4y);
 end