Solution
= Solution
For the <squared-denominator population map>, a <fixed point> satisfies
$$
\bar x=\frac{r\bar x}{(b+\bar x)^2}.
$$
There is always the extinction <fixed point> $\bar x=0$. For a positive <fixed point>, divide by $\bar x$ and use $b+\bar x>0$ to obtain
$$
\boxed{\bar x=\sqrt r-b,\qquad r>b^2}.
$$
At equality the candidate merges with zero and is not positive.