Draw the vector field and eigenvectors in the phase portrait for Van der Pol ODE

I have the follwing system which represent the Van der Pol oscillator with the inital condition and parameters are given. I draw the phase porrait using plot and ode45 but dont know how to draw the vector field and the eigenvectors with direction on them.

%function to solve the system with the time dependent term zero
function [dxdt] = vdp1(t,x,lambda,gamma,omega)
dxdt=zeros(2,1);
dxdt(1)=x(2);
dxdt(2)=lambda.*(1-x(1)^2)*x(2)-x(1)+gamma.*sin(omega*t);

end


%function to solve the system with the time dependent not zero
function [dxdt] = myode(t,x,gt,g,lambda,gamma,omega)
g=interp1(gt,g,t);
dxdt=zeros(2,1);
dxdt(1)=x(2);
dxdt(2)=lambda.*(1-x(1)^2)*x(2)-x(1)+g;
end

%script

lambda=[0.01 0.1 1 10 100] ;
gamma=[0  0.25];
omega=[0  1.04  1.1];
x0=[1   0];
x01=[3   0];
tspan=[0 500];
tspan1=[0 100];
%Numerical solution for the first initial value
[t,x]=ode45(@(t,x) vdp1(t,x,lambda(1),gamma(1),omega(1)),tspan,x0);

%Numerical solution for the second initial value
[t1,x1]=ode45(@(t,x) vdp1(t,x,lambda(1),gamma(1),omega(1)),tspan,x01);
%plotting x1,x2 aginst t

figure(3)
plot(x(:,1),x(:,2),'g-.')
hold on;
plot(x1(:,1),x1(:,2),'r-.')
xlabel('x1');
ylabel('x2')
legend('Solution first initial condition','Solution with the second initial condition')
title('phase portrait with t=[0 500] ,gamma=0,omega=0,lambda=0.01')


[tt1,xx1]=ode45(@(t,x) vdp1(t,x,lambda(2),gamma(1),omega(1)),tspan1,x0);
[tt2,xx2]=ode45(@(t,x) vdp1(t,x,lambda(3),gamma(1),omega(1)),tspan1,x0);
[tt3,xx3]=ode45(@(t,x) vdp1(t,x,lambda(4),gamma(1),omega(1)),tspan1,x0);
[tt4,xx4]=ode45(@(t,x) vdp1(t,x,lambda(5),gamma(1),omega(1)),tspan1,x0);

[tt11,xx11]=ode45(@(t,x) vdp1(t,x,lambda(2),gamma(1),omega(1)),tspan1,x01);
[tt22,xx22]=ode45(@(t,x) vdp1(t,x,lambda(3),gamma(1),omega(1)),tspan1,x01);
[tt33,xx33]=ode45(@(t,x) vdp1(t,x,lambda(4),gamma(1),omega(1)),tspan1,x01);
[tt44,xx44]=ode45(@(t,x) vdp1(t,x,lambda(5),gamma(1),omega(1)),tspan1,x01);


  

figure(6)
plot(xx1(:,1),xx1(:,2),'g-.')
hold on;
plot(xx11(:,1),xx11(:,2),'r-.')
xlabel('x1');
ylabel('x2')
legend('Solution first initial condition','Solution with the second initial condition')
title('phase portrait with t=[0 100] ,gamma=0,omega=0,lambda=0.1')



figure(8)
plot(xx2(:,1),xx2(:,2),'g-.')
hold on;
plot(xx22(:,1),xx22(:,2),'r-.')
xlabel('x1');
ylabel('x2')
legend('Solution first initial condition','Solution with the second initial condition')
title('phase portrait with t=[0 100] ,gamma=0,omega=0,lambda=1')





figure(10)
plot(xx3(:,1),xx3(:,2),'g-.')
hold on;
plot(xx33(:,1),xx33(:,2),'r-.')
xlabel('x1');
ylabel('x2')
legend('Solution first initial condition','Solution with the second initial condition')
title('phase portrait with t=[0 100] ,gamma=0,omega=0,lambda=10')


 figure(12)
plot(xx4(:,1),xx4(:,2),'g-.')
hold on;
plot(xx44(:,1),xx44(:,2),'r-.')
xlabel('x1');
ylabel('x2')
legend('Solution first initial condition','Solution with the second initial condition')
title('phase portrait with t=[0 100] ,gamma=0,omega=0,lambda=100')


 
 gt=[0  500];
 g=gamma(2).*sin(omega(2).*gt);
g1=gamma(2).*sin(omega(3).*gt);
opts = odeset('RelTol',1e-2,'AbsTol',1e-4);
[t2,x2]=ode45(@(t,x) myode(t,x,gt,g,lambda(1),gamma(2),omega(2)),tspan,x0,opts);
[t22,x22]=ode45(@(t,x) myode(t,x,gt,g,lambda(1),gamma(2),omega(2)),tspan,x01,opts);

[t3,x3]=ode45(@(t,x) myode(t,x,gt,g,lambda(1),gamma(2),omega(3)),tspan,x0,opts);
[t33,x33]=ode45(@ (t,x) myode(t,x,gt,g1,lambda(1),gamma(2),omega(3)),tspan,x01,opts);


figure(14)
plot(x2(:,1),x2(:,2),'g-.')
 hold on;
plot(x22(:,1),x22(:,2),'r-.')
xlabel('x1');
ylabel('x2')
legend('Solution first initial condition','Solution with the second initial condition')
title('phase portrait with t=[0 500] ,gamma=0.25,omega=1.04,lambda=0.01')

 
figure(16)
plot(x3(:,1),x3(:,2),'g-.')
 hold on;
plot(x33(:,1),x33(:,2),'r-.')
xlabel('x1');
ylabel('x2')
legend('Solution first initial condition','Solution with the second initial condition')
title('phase portrait with t=[0 500] ,gamma=0.25,omega=1.1,lambda=0.01')


 
 

[Jan]

I'm not going to post an answer as long as you delete questions after answers have been given. Please participate fairly in the forum.

[F.O]

I don't delete any questions without a good reason.

[John D'Errico]

You did not even give people a chance to answer your last question.

[F.O]

which question ? The one with one line answer? If it is that . the whole question was about drawing the phase portrait with odesett ,odephase 2 which I asked how to change the color of the plot but then later I find out that it is easier to just plot it using plot command and therfore I that question is not relevant very much now and anyway no one would answer it.

I am not deleting any question to be rude and I do appreciate the help I got here.

one of you you here deleted my question when I was actually trying to edit it and add my attempt code . He sayed that this place is not a homework solving. I am here presenting my attempt and asking a specific question.

[Jan]

@F.O: The forum reacts allergic to users, who overwrite their questions with "kkklllllll" and "mmmmmmmmmm​mmmmmmmmmm​mmmmmmmmmm". If somebody does this, he or she is obviously aware, that a standard deleting is not possible and wanting. Then replacing the contents with junk is not a fair usage of the forum.

It is another problem, that your question was deleted during you edited it. Here I agree with you that it is better to ask "what have you done so far" instead of deleting the question. You hzave provided your code and there is no doubt that you have spent effort to soolve your problem.

@Editor, who has deleted the former question of F.O: Please post a comment instead of deleting a question too fast.

[F.O]

I agree that wasn't a good way to get rid of unwanted questions. One other mathematical forum like math.stackexchange.com one can delete a question (there is an option) but the community can refuse to delet it.

[Jan]

This works here also: Simply add a comment or a flag and ask for deleting. The editors and admins will care for this as long as no answers have been given.

[F.O]

I did that but didnt get anything.

[F.O]

@Jan They restore my previous question ? which I replaced it by junk because no one would delet it.

Are you happy now?

Anyway I learned something here.

Answer 1

[Agnish Dutta]

If you can calculate the vector field values at every point, then the resulting data can be plotted using the “quiver” function, the details of which are in the following document:

Quiver function - https://www.mathworks.com/help/matlab/ref/quiver.html

I also found a few useful resources on the internet pertinent to what you are trying to do. Refer to the “computing the vector field” section of the following website:

http://matlab.cheme.cmu.edu/2011/08/09/phase-portraits-of-a-system-of-odes/

I believe that the following MATLAB answers page has an accepted answer relevant to your question:

https://stackoverflow.com/questions/42969046/how-to-draw-the-direction-field-of-van-der-pol-oscillator