This paper is concerned with a diffusive predator–prey system with multiple Allee effects induced by fear factors subject to Neumann boundary conditions. Firstly, we introduce a priori estimates of non-negative and non-trivial solutions. Moreover, nonexistence of non-constant positive solutions are shown for certain parameters ranges. Secondly, we study the stability of non-negative constant solutions by the linearized theory. Then, by choosing the Allee threshold $\theta$ as the bifurcation parameter, we investigate the spatially homogeneous and non-homogeneous periodic solutions as well as non-constant steady-state solutions. Finally, some theoretical results are illustrated by numerical simulations.

本文涉及的是具有诺伊曼边界条件的恐惧因素引起的具有多种Allee效应的扩散捕食者－食饵系统。首先，我们介绍了非负非平凡解的先验估计。此外，对于某些参数范围，显示了非恒定正解的不存在。其次，我们利用线性化理论研究了非负常数解的稳定性。然后，通过选择Allee阈值$\theta$作为分叉参数，我们研究了空间齐次和非齐次周期解以及非恒定稳态解。最后，通过数值模拟说明了一些理论结果。