This paper investigates the existence of positive periodic solutions for a periodic predator-prey model with fear effect and general functional responses. The general functional responses can cover the Holling types II and III functional response, the Beddington–DeAngelis functional response, the Crowley–Martin functional response, the ratio-dependent type with Michaelis–Menten type functional response, etc. Some new sufficient conditions for the existence of positive periodic solutions of the model are obtained by employing the continuation theorem of coincidence degree theory and some ingenious estimation techniques for the upper and lower bounds of the a priori solutions of the corresponding operator equation. Our results considerably improve and extend some known results.

本文研究了具有恐惧效应和一般功能反应的周期性捕食者-猎物模型的正周期解的存在性。一般功能反应可涵盖 Holling II 型和 III 型功能反应、Beddington-DeAngelis 功能反应、Crowley-Martin 功能反应、比率依赖型与 Michaelis-Menten 型功能反应等。一些新的充分条件利用重合度理论的连续定理和对相应算子方程先验解上下界的巧妙估计技术，得到了模型正周期解的存在性。我们的结果大大改进和扩展了一些已知结果。