>    restart;

>    with(DEtools):

>    kappa:=2: g:=1:

>    de1 := diff(u(t),t) = u(t)*(1-u(t)/kappa)-u(t)*v(t);

de1 := diff(u(t),t) = u(t)*(1-1/2*u(t))-u(t)*v(t)

>    de2 := diff(v(t),t) = g*(u(t)-1) * v(t);

de2 := diff(v(t),t) = (u(t)-1)*v(t)

>    dfieldplot([de1,de2], [u(t), v(t)], t=0..1, u=0..2, v=0..0.8);

[Maple Plot]

>    de3:=diff(u(t),t) = v(t)/sqrt(u(t)^2+v(t)^2);

de3 := diff(u(t),t) = v(t)/(u(t)^2+v(t)^2)^(1/2)

>    de4:=diff(v(t),t) = -u(t)/sqrt(u(t)^2+v(t)^2);

de4 := diff(v(t),t) = -u(t)/(u(t)^2+v(t)^2)^(1/2)

>    dfieldplot([de3,de4], [u(t), v(t)], t=0..1, u=-1..1, v=-1..1);

[Maple Plot]

>    de5:=diff(u(t),t) = -u(t)/sqrt(u(t)^2+v(t)^2);

de5 := diff(u(t),t) = -u(t)/(u(t)^2+v(t)^2)^(1/2)

>    de6:=diff(v(t),t) = v(t)/sqrt(u(t)^2+v(t)^2);

de6 := diff(v(t),t) = v(t)/(u(t)^2+v(t)^2)^(1/2)

>    dfieldplot([de5,de6], [u(t), v(t)], t=0..1, u=-1..1, v=-1..1);

[Maple Plot]

>