How to add trajectory into a phase plane?

Question

Alex 2014-2-24

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https://ww2.mathworks.cn/matlabcentral/answers/118837-how-to-add-trajectory-into-a-phase-plane

回答： Sundas Mustafa 2015-3-13

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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Answer 1

Mischa Kim 2014-2-24

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https://ww2.mathworks.cn/matlabcentral/answers/118837-how-to-add-trajectory-into-a-phase-plane#answer_125898

编辑：Mischa Kim 2014-2-24

在 MATLAB Online 中打开

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

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Mischa Kim 2014-2-24

编辑：Mischa Kim 2014-2-24

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 2014-3-11

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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Answer 2

Sundas Mustafa 2015-3-13

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https://ww2.mathworks.cn/matlabcentral/answers/118837-how-to-add-trajectory-into-a-phase-plane#answer_171193

use Quiver command for phase portrait. educ.jmu.edu/~strawbem/Phase_how_to.pdf

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Answer 3

Xiwen Yuan 2014-11-5

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/118837-how-to-add-trajectory-into-a-phase-plane#answer_157765

编辑：Xiwen Yuan 2014-11-5

在 MATLAB Online 中打开

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