How to add trajectory into a phase plane?

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]

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

[Alex]

Hey there again, um, it seems not working correctly this time.

[Mischa Kim]

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]

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?

Answer 2

[Sundas Mustafa]

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

Answer 3

[Xiwen Yuan]

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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