Question

Sketch the nullclines in the xy-phase plane, identify the steady sates, and draw direction arrows on the nullclines for the following system of first order equations:
\[\left\{\begin{matrix} x'=xy(1-x)\\ y'=y(1-\frac{y}{x}) \end{matrix}\right.\]

Answer 1

Here is what i got so far and am not sure if am correct
\[x-nullcline: x=0, y=0, x=1\]
\[y-nullcline: y=0, y=x\]