Example from Class based on Section 9.3

Below is the example I did in class: x'(t) = -x+y+2 y'(t)=xy. Sure looks like the basin of attraction for (0,-2) is the open lower half-plane: { (x,y)  |  y<0 }.

[Maple Plot]

 

Ignore the commands below. I used MAPLE not MATLAB. I just want to save my work for my own use.

>    field:=plots[fieldplot]([-x+y+2,x*y],x=-5..5,y=-5..5,color=blue,thickness=2,arrows=slim,title="x'=-x+y+2  &  y'=xy"):

>    curves:=phaseportrait([D(x)(t)=-x(t)+y(t)+2,D(y)(t)=x(t)*y(t)],
[x(t),y(t)],t=-5..7,
[[x(0)=5,y(0)=0],[x(0)=-5,y(0)=0],[x(0)=2.1,y(0)=0.2],
[x(0)=5,y(0)=.03],[x(0)=2,y(0)=-0.01],
[x(0)=0,y(0)=-1],
[x(0)=0,y(0)=-4],[x(0)=0,y(0)=-5],[x(0)=0,y(0)=1],[x(0)=-3,y(0)=-1],
[x(0)=0,y(0)=2],[x(0)=0,y(0)=3.5],[x(0)=-4,y(0)=1]],
x=-5..5,y=-5..5,arrows=none,stepsize=.1,
linecolor=red):

>    display(field,curves);