How can I create a phase plane for Van der Pol equation using the following showed on the picture?

I can not figure out how to create a phase plan for the Van der Pol equation using different values of k as shown on the picture.

[Mischa Kim]

I cannot see the picture. Please share the code you have developed so far.

Answer 1

[KSSV]

Note that phase plot is nothing but plot of displacement vs velocity.

function VanderPol()

[t,y] = ode23(@vdp1,[0 20],[2; 0]);

plot(t,y(:,1),'-o',t,y(:,2),'-o')
title('Solution of van der Pol Equation (\mu = 1) with ODE23');
xlabel('Time t');
ylabel('Solution y');
legend('y_1','y_2')

figure
plot(y(:,1),y(:,2))
title('Phase plane plot')
end
function dydt = vdp1(t,y)
%VDP1  Evaluate the van der Pol ODEs for mu = 1
%
%   See also ODE113, ODE23, ODE45.

%   Jacek Kierzenka and Lawrence F. Shampine
%   Copyright 1984-2014 The MathWorks, Inc.

dydt = [y(2); (1-y(1)^2)*y(2)-y(1)];
end

Answer 2

[andargie]

analysis

Answer 3

[andargie]

anaysis