Stabilization of population dynamics via threshold harvesting strategies

We study two different harvesting/thinning control strategies in the framework of one-dimensional discrete time population models. They have the common feature of considering a threshold population size, commonly called Biomass at the limit, under which the population is not altered, and they differ in how the harvesting/thinning is applied when that threshold is surpassed: one uses the well known proportional feedback control, whereas the other employs the recently proposed target oriented control. We focus on the possibility of applying these strategies to control the chaotic behaviour predicted by some one-dimensional discrete time population models. We discuss the basic properties of both strategies and compare them with other simpler control methods. Particularly, we show that increasing the threshold does not affect, or almost does not affect, a stable exploited population as long as the threshold is lower than the carrying capacity of the system.