Consider the system of differential equations
$$\dot {x}=y-x^2$$ $$\dot {y}=x-y$$
a. Determine the fixed points
(1,1) (0,0)
b. Determine the nullclines and the signs of $\dot {x}$ and $\dot {y}$ in the various regions of the plane.
x-nullcline: $y=x^2$
y-nullcline: $y=x$
Does everything look correct?