How to add trajectory into a phase plane?
10 views (last 30 days)
Show older comments
Hi, I have the code below of my function phase plane and it works fine. I want to add some trajectories into my phase plane, how am I able to do it?
function my_phase()
[~,X] = ode45(@EOM,[0 50],[1 1]);
u = X(:,1);
w = X(:,2);
plot(u,w)
xlabel('u')
ylabel('w')
grid
end
function dX = EOM(t, y)
dX = zeros(2,1);
u = y(1);
w = y(2);
A = 1;
B = 1;
dX = [w*u^2 - B*u;...
A - w - w*u^2];
end
It is my original phase plane
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/157493/image.bmp)
And I want my phase plane like this:
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/157495/image.png)
%
0 Comments
Accepted Answer
Mischa Kim
on 24 Feb 2014
Edited: Mischa Kim
on 24 Feb 2014
Like this?
function my_phase()
IC = [1 1; 1 2;1 3;1 4];
hold on
for ii = 1:length(IC(:,1))
[~,X] = ode45(@EOM,[0 50],IC(ii,:));
u = X(:,1);
w = X(:,2);
plot(u,w,'r')
end
xlabel('u')
ylabel('w')
grid
end
function dX = EOM(t, y)
dX = zeros(2,1);
u = y(1);
w = y(2);
A = 1;
B = 1;
dX = [w*u^2 - B*u;...
A - w - w*u^2];
end
3 Comments
Mischa Kim
on 24 Feb 2014
Edited: Mischa Kim
on 24 Feb 2014
What do you mean by not working correctly? Do you get an error msg, or, the plot does not look like the one you posted for the simple harmonic oscillator?
You only replace the first function, keep the second. See above.
More Answers (2)
Sundas Mustafa
on 13 Mar 2015
use Quiver command for phase portrait. educ.jmu.edu/~strawbem/Phase_how_to.pdf
0 Comments
Xiwen Yuan
on 5 Nov 2014
Edited: Xiwen Yuan
on 5 Nov 2014
Hey, i have another answer to replace the first function with the following
function my_phase()
IC = [1 1; 1 2;1 3;1 4];
hold on
for ii = 1:length(IC(:,1))
[~,X] = ode45(@EOM,[0 50],IC(ii,:));
u = X(:,1);
w = X(:,2);
plot(u,w,'r')
u = gradient(X(:,1));
v = gradient(X(:,2));
quiver(X(:,1),X(:,2),u,v);
end
xlabel('u')
ylabel('w')
grid
end
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/176492/image.png)
%
0 Comments
See Also
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!