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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:
%

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 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
%

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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