Neimark-Sacker bifurcations in a host-parasitoid system with a host refuge

In this work, the effect of a host refuge on a host-parasitoid inter- action is investigated. The model is built upon a modied Nicholson-Bailey system by assuming that in each generation a constant proportion of the host is free from parasitism. We derive a sucient condition based on the model parameters for both populations to coexist. We prove that it is possible for the system to undergo a supercritical and then a subcritical Neimark-Sacker bifurcation or for the system only to exhibit a supercritical Neimark-Sacker bifurcation. It is illustrated numerically that a constant proportion of host refuge can stabilize the host-parasitoid interaction.