= Harvested bistable population thresholds
{title2=$E_T=P(0),\quad E_M=\max_{a_2<N<a_3}P(N)$}
For $\dot N=N[P(N)-E]$ and $P(N)=\prod_{i=1}^3(a_i-N)$ with $0<a_1<a_2<a_3$, extinction changes stability at $E_T$, while the upper stable population and an unstable separator merge at $E_M$. If $E_T<E_M$, an interval of efforts supports stable extinction and a stable positive population simultaneously; at $E_M$ the positive state collapses. If the thresholds have the opposite order, the high-population pair disappears before the lower stable branch reaches extinction. At a positive <equilibrium> stability follows from the sign of $NP'(N)$.
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