Extinction domain

For $\alpha>\frac{\sigma^{2}}{4\left(n\sigma +1 \right)}$, there is an extinction domain around the diagonal $x_1=..=x_n$. Simulations show that the domain is very restricted until $\alpha$ becomes very close to its upper threshold value, at which non-0 equilibria cease to exist (see Figures 9 and 10).