= Constant-quota harvested logistic growth
{title2=$\dot N=rN(1-N/K)-h$}
For a fixed catch rate $h$, natural logistic growth can replace the catch at two abundances if $0<h<rK/4$. The upper <equilibrium> $N_+=K[1+\sqrt{1-4h/(rK)}]/2$ attracts, and the lower $N_-$ is an unstable survival threshold. They meet in a <saddle-node bifurcation> at $h=rK/4$, $N=K/2$. Above this catch every positive population declines to zero. Below it a population initially under $N_-$ also becomes extinct. A constant catch is stopped at extinction to avoid negative abundances; it is distinct from per-capita harvesting proportional to $N$.
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