How to add trajectory into a phase plane?
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Alex
le 24 Fév 2014
Réponse apportée : Sundas Mustafa
le 13 Mar 2015
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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Réponse acceptée
Mischa Kim
le 24 Fév 2014
Modifié(e) : Mischa Kim
le 24 Fév 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 commentaires
Mischa Kim
le 24 Fév 2014
Modifié(e) : Mischa Kim
le 24 Fév 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.
Plus de réponses (2)
Sundas Mustafa
le 13 Mar 2015
use Quiver command for phase portrait. educ.jmu.edu/~strawbem/Phase_how_to.pdf
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Xiwen Yuan
le 5 Nov 2014
Modifié(e) : Xiwen Yuan
le 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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