I want to draw the bifurcation diagram fro the model.
dx/dt=rx(1-x/K)-mxy/(ax+by+c) dy/dt=emxy/(ax+by+c)-dy-hy^2.
parameters are all +ve.
I have tryed to plot it but fails.
clearr=0.806; a=15; b=16;c=17;e=0.333;d=0.3;h=0.01;K=200;x (1)=0.7;y (1)=0.11;t (1)=0;for m=6:1:22for i=1:10000 t (i+1)=t (i)+.01; x (i+1)= x (i)+0.01*[r*x (i)*(1-x (i)/K)-m*x (i)*y (i)/(a*x \(i)+b*y (i)+c)]; y (i+1)=y (i)+.01*[e*m*x (i)*y (i)/(a*x (i)+b*y (i)+c)-d*y (i)-h*y \(i)^2]; endplot (m,x, 'b')hold on; endxlabel ('m')ylabel ('x')figure (2)for m=6:1:22for i=1:10000 t (i+1)=t (i)+.01; x (i+1)= x (i)+0.01*[r*x (i)*(1-x (i)/K)-m*x (i)*y (i)/(a*x \(i)+b*y (i)+c)]; y (i+1)=y (i)+.01*[e*m*x (i)*y (i)/(a*x (i)+b*y (i)+c)-d*y (i)-h*y \(i)^2]; endplot (m,y, 'b')hold on; endxlabel ('m')ylabel ('y')
Please modify or help me to modify the matlab code to draw the following bifurcation diagram (parameter VS population):
1.Transcritical bifurcation (x vs m & y vs. m) around at m= 13.666
2. Saddle-node bifurcation (x vs m & y vs. m) around at m = 20.8.
3. Hopf-bifurcation (x vs m & y vs. m) at m=14.73, (d,h) = (0.02,0.001) and others are same.
Best Answer