Solution
= Solution
At a nonzero <fixed point>, both bracketed per-capita growth rates vanish:
$$
-\epsilon_1+\alpha N_2^*=0,
\qquad
\epsilon_2-\alpha N_1^*=0.
$$
Hence the coexistence equilibrium of this <Lotka-Volterra predator-prey model> is
$$
\boxed{(N_1^*,N_2^*)=\left(\frac{\epsilon_2}{\alpha},\frac{\epsilon_1}{\alpha}\right)}.
$$