GLOBAL ANALYSIS OF A HARVESTED PREDATOR-PREY MODEL INCORPORATING A CONSTANT PREY REFUGE

A predator-prey model with Holling type II functional response incorporating a constant prey refuge and independent harvesting in either species is investigated. Some sufficient conditions of the instability and stability properties to the equilibria and the existence and uniqueness to limit cycles for the model are obtained. We also show that influence of prey refuge and harvesting efforts on equilibrium density values. One of the surprising finding is that for fixed prey refuge, harvesting has no influence on the final density of the prey species, while the density of predator species is decreasing with the increasing of harvesting effort on prey species and the fixation of harvesting effort on predator species. Numerical simulations are carried out to illustrate the obtained results and the dependence of the dynamic behavior on the harvesting efforts or prey refuge.