Bifurcations in a Leslie–Gower model with constant and proportional prey refuge at high and low density

Abstract

Assuming that the prey refuge is proportional to the prey density if its population size is below a critical threshold, or constant if its size is above the threshold, this paper proposes, and qualitatively analyzes, a Leslie–Gower predator–prey model assuming alternative feeding and harvesting in predators, and a Holling II function as the predator functional response. From the results of the mathematical analysis to the predator–prey models with proportional or constant prey refuge, the proposed model retains the same bifurcation cases obtained for each model analyzed. However, appropriate alterations of the parameters representing the critical threshold of prey population size and harvest in predators allows the formation of at least one limit cycle, stable or unstable, that lives in both vector fields of the proposed model.