 Fixed-quota harvesting of Lotka-Volterra populations

In logarithmic prey/predator coordinates, the Lotka-Volterra predator-prey model has divergence zero. Removing a fixed prey quota $h$ changes $\log X$ to $\log (X-h)$ and expands logarithmic area by $X/(X-h)$. Thus a periodic annually harvested orbit has an expanding return map determinant and cannot be asymptotically stable. A continuous-quota approximation gives a coexistence equilibrium with positive Jacobian matrix trace $h/X_{\ast }$, unlike proportional harvesting, which only changes the prey growth parameter in this idealized model.