Constant-effort harvesting ($\dot{N}=h(N)-EN$)

Constant harvest effort removes individuals at rate proportional to their current population, with fixed coefficient $E$. Its continuous model subtracts $EN$ from the growth rate, while a discrete model may use $N_{t+1}=g(N_t)-E{N}_t$. This differs from constant-quota harvesting, which subtracts a population-independent amount. A discrete rule must remain nonnegative on its physical state range, or require a separately specified truncation.

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 $N{P}^{\prime }(N)$.