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3d phase portrait

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Hi, I want to plot a 3-d phase portrait for a set of 3 ODEs, i have used the following code and i get a basic plot, i was wondering how to add direction arrows and a mesh grid and why i only get single spirals for the trajectories. Here is the code i have used:
function f = cluster(t,y)
%equilibrium values
%c1 equilbrium value
f = zeros(size(y));
f(1) = -50*a*y(1)-b*y(1)+15*a*y(1)*y(2)+20*a*y(2)*y(3)+y(2)*b+9*a*y(2)^2+6*a*y(1)^2-60*a*y(2)-80*a*y(3)+24*a*y(2)*y(3)+16*a*y(3)^2;
f(2) = 10*a*y(1) - a*y(1)*y(2) -4*a*y(1)*y(3) -2*a*y(1)^2 -b*y(2) +3*a*y(2)^2 -10*a*y(2) +4*a*y(2)*y(3) +b*y(3);
f(3) = -2*a*y(1)*y(2) - 3*a*y(2)^2 -4*a*y(2)*y(3) +10*a*y(2)-b*y(3);
Plotting code:
[t,y] = ode45(@cluster,[0:0.01:1],[1 2 3]);
plot(t,y(:,3)); % plot of z(t) versus time
plot(y(:,1),y(:,3)); % plot of z versus x
plot3(y(:,1),y(:,2),y(:,3)); % 3D plot of trajectory
plot(y(:,1),y(:,2)); % plot of z versus x
I have computed the corresponding eigen values and vector points for specific equilbrium points in a separate file not sure if that will help?


Akshay Khadse
Akshay Khadse on 31 Aug 2018
Can you elaborate on what is the "f" in your code above? According to me, for a phase portrait, "f" should be the gradients. However, you are plotting the solution of the differential equations, hence the single spirals.
Gulmira Tussupbekova
Gulmira Tussupbekova on 2 Apr 2020
Can you please send a code for this problem

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Accepted Answer

Akshay Khadse
Akshay Khadse on 31 Aug 2018
Edited: Akshay Khadse on 31 Aug 2018
You can get 3D Phase Portraits by plotting the gradients against the co-ordinates using the " meshgrid ", and " quiver3 " functions.
" meshgrid " is used to generate the 2D or 3D grids and " quiver " or " quiver3 " is used to place arrows at these co-ordinates.
Creating meshgrid:
[x1,y1,z1] = meshgrid(-2:0.2:2,-2:0.2:2,-2:0.2:2);
u = zeros(size(x1));
v = zeros(size(y1));
w = zeros(size(z1));
Calculating gradients:
for i = 1:numel(x1)
Yprime = cluster(t,[x1(i); y1(i); z1(i)]);
u(i) = Yprime(1);
v(i) = Yprime(2);
w(i) = Yprime(3);
quiver3(x1,y1,z1,u,v,w); figure(gcf)
Please refer to the documentation for "quiver3" here for examples.

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Aishah Malek
Aishah Malek on 2 Sep 2018
This makes sense , thankyou for you help

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