restart;with(plots):with(plottools):with(DEtools):with(linalg):E1:=diff(x(t),t)=x(t)*(1-y(t));E2:=diff(y(t),t)=.3*y(t)*(x(t)-1);DEplot([diff(x(t),t)=x(t)*(1-y(t)),diff(y(t),t)=.3*y(t)*(x(t)-1)],[x(t),y(t)], t=-8..8,[[x(0)=1.2,y(0)=1.2],[x(0)=1,y(0)=.7]],stepsize=.2);dfieldplot([diff(x(t),t)=x(t)*(1-y(t)),diff(y(t),t)=.3*y(t)*(x(t)-1)],[x(t),y(t)], t=-6..6,x=-3..3,y=-3..3);A:=matrix(2,2,[1,0,0,-.3]);eigenvalues(A);eigenvectors(A);L1:=diff(x(t),t)=x(t);L2:=diff(y(t),t)=-.3*y(t);dfieldplot([L1,L2],[x(t),y(t)], t=-5..5,x=-3..3,y=-3..3);B:=matrix(2,2,[0,-1,.3,0]);eigenvalues(B);eigenvectors(B);L3:=diff(x(t),t)=-y(t);L4:=diff(y(t),t)=.3*x(t);dfieldplot([L3,L4],[x(t),y(t)], t=-5..5,x=-3..3,y=-3..3);