Maple Worksheet to go with the HW on Nonlinear Systems. with(DEtools): with(plots): Prob07a:=[diff(x(t),t)=x(t)*((3/2)-x(t)-(1/2)*y(t)),diff(y(t),t)=y(t)*(2-y(t)-(3/4)*x(t))]; DEplot(Prob07a,[x(t),y(t)],t=0..10,x=0..2,y=0..2,[[x(0)=1,y(0)=1],[x(0)=1,y(0)=1/2],[x(0)=1,y(0)=2],[x(0)=0.2,y(0)=0.1],[x(0)=0.1,y(0)=0.5]],stepsize=0.01); Prob07b:=[diff(x(t),t)=cos(y(t)),diff(y(t),t)=sin(x(t))]; DEplot(Prob07b,[x(t),y(t)],t=-1..10,x=-8..8,y=-8..8,dirgrid=[40,40],[[x(0)=1,y(0)=1],[x(0)=0,y(0)=4]],stepsize=0.01); Prob07c:=[diff(x(t),t)=x(t)*(1-(1/2)*x(t)-(1/2)*y(t)),diff(y(t),t)=y(t)*(-(1/4)+(1/2)*x(t))]; DEplot(Prob07c,[x(t),y(t)],t=0..10,x=0..3,y=0..3,[[x(0)=1,y(0)=1],[x(0)=1,y(0)=1/2],[x(0)=1,y(0)=2],[x(0)=0.2,y(0)=0.1],[x(0)=0.1,y(0)=0.5]],stepsize=0.01); Prob07d:=[diff(x(t),t)=x(t)*(1-x(t)-y(t)),diff(y(t),t)=y(t)*((3/2)-y(t)-x(t))]; DEplot(Prob07d,[x(t),y(t)],t=0..10,x=0..2,y=0..2,[[x(0)=1,y(0)=1],[x(0)=1,y(0)=1/2],[x(0)=1,y(0)=2],[x(0)=0.2,y(0)=0.1],[x(0)=0.1,y(0)=0.5]],stepsize=0.01);