In this study, we consider a diffusive predator–prey model with multiple Allee effects induced by fear factors. We investigate the existence, boundedness and permanence of the solution of the system. We also discuss the existence and non-existence of non-constant solutions. We derive sufficient conditions for spatially homogeneous (non-homogenous) Hopf bifurcation and steady state bifurcation. Theoretical and numerical simulations show that strong Allee effect and fear effect have great effect on the dynamics of system.

中文翻译：

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具有 Allee 和恐惧效应的扩散捕食者 - 猎物模型的定性分析

在这项研究中，我们考虑了一种由恐惧因素引起的具有多种 Allee 效应的扩散捕食者 - 猎物模型。我们研究系统解的存在性、有界性和持久性。我们还讨论了非常数解的存在和不存在。我们推导出空间均匀（非均匀）Hopf 分岔和稳态分岔的充分条件。理论和数值模拟表明，强阿利效应和恐惧效应对系统动力学有很大影响。