3D Phase portrait for a set of differential equations

Question

Vira Roy 2020-4-25

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/520612-3d-phase-portrait-for-a-set-of-differential-equations

评论： Vira Roy 2020-4-25

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

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darova 2020-4-25

Phase portrait it's a graph

and y. HOw to plot 3D phase portrait? What those axes represent

Her is the link from wikipedia: LINK

Vira Roy 2020-4-25

编辑：Vira Roy 2020-4-25

Thanks for reply darova. I was trying to do as Lorenz attractor done by James adams in this code. I have three differential equations and wanted to get a plot similar to above one i have shown.

What I wanted to ask is that, Can we get that by just choosing some initial conditions and plot the three solutions against each other. If not If have to get a phase portrait in 3 dimensions how should I proceed.

Those axes represent the three variables in the differential equation. I, n and A. Similar to x ,y ,z in Lorentz attractor.

Thank you anyways Darova.

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