How to add trajectory into a phase plane?
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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)
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Risposta accettata
Mischa Kim
il 24 Feb 2014
Modificato: Mischa Kim
il 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 Commenti
Mischa Kim
il 24 Feb 2014
Modificato: Mischa Kim
il 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.
Più risposte (2)
Sundas Mustafa
il 13 Mar 2015
use Quiver command for phase portrait. educ.jmu.edu/~strawbem/Phase_how_to.pdf
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Xiwen Yuan
il 5 Nov 2014
Modificato: Xiwen Yuan
il 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)
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