Exploring the predator–prey linkage in food chain system is the most familiar research work in population biology. Recently, some research experiments show that predator–prey interaction not only governed by direct hunting but also influenced by some indirect effect such as fear effect (felt by prey) that may change the physiological behavior of prey. Based upon this fact, we consider a tritrophic food chain model incorporating with anti-predation response (fear effect) and multiple time delays for biomass conversion from prey to middle predator and middle to top predator. We analyze the resulting delay differential equations and explore how the anti-predation response level affects the population dynamics. We also investigate the effect of delay parameters, for which the model system switches its stability through Hopf-bifurcation. We compare all of our results between two different food chain models consisting of two different functional responses. Some numerical simulations are performed to validate the effectiveness of the derived theoretical results.

中文翻译：

---

具有多重延迟和抗捕食作用的两种三营养食物链模型的比较

探索食物链系统中的捕食者-猎物联系是种群生物学中最为人熟知的研究工作。最近，一些研究实验表明，捕食者与猎物的相互作用不仅受直接狩猎的支配，而且还受到一些间接效应的影响，例如恐惧效应（被猎物感受到）可能会改变猎物的生理行为。基于这一事实，我们考虑了一个三营养食物链模型，该模型结合了反捕食反应（恐惧效应）和从猎物到中间捕食者和中间到顶级捕食者的生物量转换的多个时间延迟。我们分析了由此产生的延迟微分方程，并探讨了反捕食响应水平如何影响种群动态。我们还研究了延迟参数的影响，模型系统通过 Hopf 分岔来切换其稳定性。我们比较了由两种不同功能反应组成的两种不同食物链模型之间的所有结果。进行了一些数值模拟以验证推导的理论结果的有效性。