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.

中文翻译：

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互干扰宿主-寄生蜂模型中的稳定性、解析分岔结构和混沌控制

在本文中，我们提出了一项关于具有 Beverton-Holt 生长的相互干扰宿主-寄生虫模型的研究。众所周知，寄生虫的相互干扰对寄主-寄生虫模型的动力学具有稳定的影响，因为搜索效率随寄生虫密度的变化在很大程度上取决于寄生虫的相互干扰。因此，我们将相互干扰功能响应纳入宿主-寄生虫模型以表征这种现象。本文研究了本模型的定性行为。首先讨论了模型不动点的存在性和局部稳定性。然后，利用摄动法和范式理论，推导出模型的 Neimark-Sacker 分岔的出现条件。此外，证明了模型在 Marotto 意义上的混沌行为。为了控制当前模型的混沌行为，我们应用OGY反馈控制策略。最后，提供数值模拟来支持我们的理论讨论。