For the nullclines, we consider x ′ = x ( 2 − x − y ) = 0 {\displaystyle \ x'=x(2-x-y)=0} : x ′ = 0 {\displaystyle \ x'=0} , if x = 0 {\displaystyle \ x=0} or y = 2 − x {\displaystyle \ y=2-x} .
Now we consider y ′ = y ( 1 − x ) = 0 {\displaystyle \ y'=y(1-x)=0} : y ′ = 0 {\displaystyle \ y'=0} , if y = 0 {\displaystyle \ y=0} or x = 1 {\displaystyle \ x=1} .
For the critical points, x ′ = y ′ = 0 {\displaystyle \ x'=y'=0} must hold. Hence, the critical points are ( x 0 , y 0 ) = ( 0 , 0 ) , ( 2 , 0 ) , ( 1 , 1 ) {\displaystyle \ (x_{0},y_{0})=(0,0),(2,0),(1,1)} .
Plotted in the phase space:
: 
, if 
or 
.
: 
, if 
or 
.
must hold. Hence, the critical points are 
.
