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')
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