Plot dynamics of an ODE

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UserCJ
UserCJ on 21 Sep 2022
Commented: Cris LaPierre on 22 Sep 2022
I have an ODE and I need to plot with respect to and varying p. Following is the sample plot required.
I managed to draw one plot for and following is the sample code.
[xi,x] = meshgrid(0:0.001:1,0:0.002:1);
p =1
f2 = @(x,a,b) a*b*(x)./(b-2+x));
f1 = @(x,a,b) a*b*(1-x)./(2*b-x);
rs = @(x1,x2,a,b,p) x1.*f1(x,a,b) - p.*(1-x1).*f2(x,a,b);
figure
contour(x1,2,rs(x1,x2,1,2,1),[0 0]);
Next I added a loop for p as follows:
np = 10;
phi = linspace(0,1,np);
for p = 1:np
f2 = @(x,a,b) a*b*(x)./(b-2+x));
f1 = @(x,a,b) a*b*(1-x)./(2*b-x);
rs = @(x1,x2,a,b,p) x1.*f1(x,a,b) - p.*(1-x1).*f2(x,a,b);
R = rs(x1,x2,1,2, p(p));
contour(x1,x2,R);
hold on
end
hold off
But, instead of the required ourput of 10 plots in one graph, I get many plots (>10) in my output. Can someone please help me with this?
  1 Comment
Cris LaPierre
Cris LaPierre on 21 Sep 2022
Edited: Cris LaPierre on 21 Sep 2022
You have not copied your code correctly here, as both examples do not run.

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Accepted Answer

Cris LaPierre
Cris LaPierre on 21 Sep 2022
I'm assuming your goal is to plot a line for when the function rs is equal to zero for various values of p. You could do that using contour, but I don't think that is the best way. However, you could still use contour to get the (x,y) coordinates of the 0 contour line for each, and then plot those.
np = 10;
[x1,x2] = meshgrid(0:0.001:1,0:0.002:1);
for p = 1:np
f2 = @(x,a,b) a*b*(x)./(b-2+x);
f1 = @(x,a,b) a*b*(1-x)./(2*b-x);
rs = @(xi,x,a,b,p) xi.*f1(x,a,b) - p.*(1-xi).*f2(x,a,b);
R = rs(x1,x2,1,2, p);
figure(1)
M=contour(x1,x2,R,[0 0]);
figure(2)
plot(M(1,2:end),M(2,2:end),'DisplayName',"p="+p)
axis([0 1 0 1])
hold on
end
hold off
legend(Location="northwest")
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