In this paper, we consider a predator–prey model with Allee effect, fear effect and prey refuge. By considering the prey refuge as a parameter, we give the threshold condition for the stability of the system, and prove that the system undergoes a supercritical Hopf bifurcation. We show that increasing the prey refuge or Allee effect can make the dynamical behavior of the system more complicated; the fear effect or Allee effect has no influence on the prey density, but can lead to a decrease of the predator population at positive equilibrium.

中文翻译：

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在带有食饵避难所的捕食者－食饵系统中模拟Allee效应和恐惧效应

在本文中，我们考虑具有Allee效应，恐惧效应和避难所的捕食者—食饵模型。通过将避难所作为参数，给出了系统稳定性的阈值条件，并证明该系统经历了超临界霍普夫分支。我们表明，增加猎物避难所或Allee效应会使系统的动力学行为更加复杂。恐惧效应或Allee效应对猎物密度没有影响，但是可以导致处于正平衡状态的捕食者数量减少。