Solution
= Solution
Set
$$
x=\frac{N_1}{K_1},\qquad y=\frac{N_2}{K_2},\qquad \tau=r_2t.
$$
Then
$$
x'=\rho x(1-x-\alpha y),\qquad
y'=y(1-\beta x).
$$
The steady states are
$$
(0,0),\qquad(1,0),\qquad
\left(\frac1\beta,\frac{1-\beta^{-1}}{\alpha}\right),
$$
where the coexistence state is biologically relevant exactly when $\beta>1$.