function lotka
    clear;clf;
    t0=0;
    tmax=15;
    a=0.01;
    b=0.02;
    y0=[20,20];
    hold on
    plot(1/b,1/a,'r*')
    [T,Y]=ode23(@ff,[t0,tmax],[y0(1),y0(2)]);
    plot(Y(:,1),Y(:,2))
    quiver(y0(1),y0(2),y0(1)-a*y0(1)*y0(2),-y0(2)+b*y0(1)*y0(2))
    function z=ff(t,y)
        z=[y(1)-a*y(1)*y(2);-y(2)+b*y(1)*y(2)];
    end
end