Stability, Analytic Bifurcation Structure and Chaos Control in a Mutual Interference Host-Parasitoid Model

Abstract

In this paper, we present a study on a mutual interference host-parasitoid model with Beverton–Holt growth. It is well known that, mutual interference of parasites has a stabilizing influence on the dynamics of the host-parasitoid model since the variance in searching efficiency, with parasite density, significantly depends on parasites’ mutual interference. Thus, we have incorporated a mutual interference functional response into a host-parasitoid model to characterize such a phenomenon. The qualitative behaviors of the present model is investigated in this paper. Firstly, the existence and local stability of the model fixed points are discussed. Then, using perturbation method and normal form theory, we derived the emergence conditions of Neimark–Sacker bifurcation of the model. Furthermore, chaotic behavior of the model in the sense of Marotto is proved. In order to control chaotic behavior of the present model, we apply OGY feedback control strategy. Finally, numerical simulations are provided to support our theoretical discussion.