Neimark–Sacker Bifurcation and Stability of a Certain Class of Host-Parasitoid Models with Host Refuge Effect

Abstract

In this paper, we consider the dynamics of a certain class of host-parasitoid models, where some hosts are completely free from parasitism either with or without a spatial refuge and the host population is governed by the Beverton–Holt equation. We assume that, in each generation, a constant portion of the host population may find a refuge and be safe from the attack by parasitoids. We derive some criteria for the Neimark–Sacker bifurcation. Then, we apply the developed theory to the three well-known cases: [Formula: see text] model, Hassel and Varley model, and parasitoid–parasitoid model. Intensive numerical calculations suggest that the last two models undergo a supercritical Neimark–Sacker bifurcation.