3D Phase portrait for a set of differential equations
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Vira Roy
el 25 de Abr. de 2020
Comentada: Vira Roy
el 25 de Abr. de 2020
I have a set of three differential equations and I want to make a phase portrait of them. I have some idea of using quiver or plot3 to get a phase portrait of a set of 3 differential equations. I am unable to do for this case.
Here is my attempt:
timerange= 0:0.5:350;
IC= [0.1,0,0];
IC1= [0.1,0.2,0];
[t,y] =ode45(@(t,y) fn(t,y),timerange, IC);
[t1,y1] =ode45(@(t,y) fn(t,y),timerange, IC1);
plot3(y(:,1),y(:,2),y(:,3));
hold on
plot3(y1(:,1),y1(:,2),y1(:,3));
grid
xlabel('T')
ylabel('A')
zlabel('I')
function rk1 =fn(t,y)
r=0.00173;K=0.03166;A0=0.4;gammaA=0.04;eps = 0.00055;rho= 0.025;alpha1= 1.30187;c1=0.63433;
I0= 0.3;gammaI=0.0208;
alpha= 0.0002802;
n= y(1);
A= y(2);
I= y(3);
rk1(1)= r*n*(1- n/K)+ alpha*A*n -eps*n*I;
rk1(2) = A0 - gammaA*A;
rk1(3) = I0 + (rho*I*n)/(alpha1+n) -c1*I*n - gammaI*I;
rk1=rk1(:);
endI
What I am doing is merely changing the initial conditions The actual result should be something like this.
Any help would be greately helpful. This is what I am getting from above code.
Thank You
2 comentarios
darova
el 25 de Abr. de 2020
Phase portrait it's a graph and y. HOw to plot 3D phase portrait? What those axes represent
Respuesta aceptada
darova
el 25 de Abr. de 2020
I tried to plot T A and I separately. X Y Z axis represents T A and I respectively. Color represents derivative of T A or I
I used surface to plot color lines (plotted curves as surfaces, made them nx2 size)
derivative just difference
3 comentarios
darova
el 25 de Abr. de 2020
- The graph I get has different colour scheme than shown in your diagram. Is that system specific or am i missing something.
It's because im from Poland. Poles like more red colors
colormap jet % try to change colormap
- The commented part of the code, what does this represent. I removed the comment and ran but found no difference in the plot.
Impossible! Maybe color axis (range) didn't after you uncommented. Try to add clf at the beginning of the script
clf
- I can only see one graph, unlike the two you have pictured above, dy/dt and dy. Do i have make some changes in the code to get that.
I just run the script, saved the picture. Then commented line and run again (save second picture)
- I am accepting the answer as it was helpful.
But i don't see any
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