This paper presents the qualitative analysis of a predator–prey model with nonmonotonic functional response and impulsive effects. Different from previous work, by considering two factors of nonmonotonic functional response and impulsive effects, this paper studies the existence and stability of the periodic semi-trivial solution $y=0$ first. Then, by constructing an appropriate Poincare map and introducing geometric theory, it is shown that the predator–prey model can exhibit a variety of dynamic phenomena, including orbitally asymptotically stable order-1 periodic solution (O1PS), order-2 periodic solution (O2PS) and globally stable equilibrium point under certain conditions. When there exists an O2PS, its appearance and disappearance as well as the appearance of bifurcation phenomenon are discussed in detail with different selections of the initial value of predator. Finally, numerical simulations illustrate the correctness of the results of the theoretical analysis. The theoretical results presented in this paper can be seen as an advancement to the previous related works.

本文介绍了具有非单调功能响应和脉冲效应的捕食者 - 猎物模型的定性分析。不同于以往的工作，本文通过考虑非单调函数响应和脉冲效应两个因素，研究了周期半平凡解的存在性和稳定性$\mathrm{是的}=0$第一的。然后，通过构建合适的庞加莱图并引入几何理论，表明捕食者-猎物模型可以表现出多种动态现象，包括轨道渐近稳定的一阶周期解（O1PS）、二阶周期解（O2PS ) 和特定条件下的全局稳定平衡点。当存在O2PS时，结合捕食者初始值的不同选择，详细讨论了O2PS的出现和消失以及分叉现象的出现。最后，数值模拟说明了理论分析结果的正确性。本文提出的理论结果可以看作是对先前相关工作的进步。