clear all;

b=0.5;a=1;F=@(t,y)[2*y(1)-a*y(1)*y(2); -y(2)+b*y(1)*y(2)];


figure(1);
[t,y]=ode45(F,[0 15],[2;3]);
plot(t,y) 


figure(2);
[r,f]=meshgrid(0:1:5,0:1:4);
rp=2*r-a*r.*f;fp=-f+b*r.*f;
quiver(r,f,rp,fp);
hold on;
plot(y(:,1),y(:,2));
%comet(y(:,1),y(:,2))
%axis tight
hold off;
% axis([0 7 0 7])
%plot(t,y)