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How to add trajectory into a phase plane?

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Alex
Alex on 24 Feb 2014
Answered: Sundas Mustafa on 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
And I want my phase plane like this:
%

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Accepted Answer

Mischa Kim
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

Alex
Alex on 24 Feb 2014
Hey there again, um, it seems not working correctly this time.
Mischa Kim
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.
Alex
Alex on 11 Mar 2014
Hey is me again, I have successfully to plot the graph, but it seems like the graph only shows the positive value, and I wonder can the trajectories toward to negative as well. Also I wonder how to add those blue arrow in my phase plane?

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More Answers (2)

Xiwen Yuan
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
%

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Sundas Mustafa
Sundas Mustafa on 13 Mar 2015
use Quiver command for phase portrait. educ.jmu.edu/~strawbem/Phase_how_to.pdf

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