  We consider a logistic differential equation subject to impulsive delayed
harvesting, where the deduction information is a function of the population
size at the time of one of the previous impulses. A close connection to the
dynamics of high-order difference equations is used to conclude that while the
inclusion of a delay in the impulsive condition does not impact the optimality
of the yield, sustainability may be highly affected and is generally
delay-dependent. Maximal and other types of yields are explored, and sharp
stability tests are obtained for the model, as well as explicit sufficient
conditions. It is also shown that persistence of the solution is not guaranteed
for all positive initial conditions, and extinction in finite time is possible,
as is illustrated in the simulations.
