How to plot phase plane in MATLAB?

Hi I have two equations here, and I wonder that how do you plot them as a phase plane.

du/dt = wu^2 - Bu dw/dt = A - w - wu^2

and A,B both are constants

Answer 1

[Mischa Kim]

Alex, assuming that you are talking about a u-w (position-velocity, sort of) phase plot, here you go. Essentially, you only need to solve the differential equations and then plot the result.

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

[Alex]

I wonder that why did you set A and B both are equal to 1?

[Mischa Kim]

Had to pick some values to do the simulation.

Answer 2

[Elistin]

fonction ma_phase()

[~,X] = ode45(@EOM,[0 50],[1 1]);

u = X(:,1);

w = X(:,2);

parcelle(u,w)

xlabel( 'u' )

ylabel( 'w' )

la grille

fin

fonction dX = EOM(t, y)

dX = zéros(2,1);

u = y(1);

w = y(2);

A = 1 ;

B = 1 ;

dX = [w*u^2 - B*u ; ...

A - w - w*u^2] ;

fin