In the predator-prey system, predators can affect the prey population (1) by direct killing and (2) by inducing predation fear, which ultimately force preys to adopt some anti-predator strategies. However, the anti-predator strategy is not the same for all individual preys of different life stages. Also, anti-predator behavior has both cost and benefit, but most of the mathematical models observed the dynamics by incorporating its cost only. In the present study, we formulate a predator-prey model dividing the prey population into two stages: juvenile and adult. We assume that adult preys are only adapting group defense as an anti-predator strategy when they are sensitive to predation. Group defense plays a positive role for adult prey by reducing their predation, but, on the negative side, it simultaneously decreases their reproductive potential. A parameter, anti-predator sensitivity is introduced to interlink both the benefit and cost of group defense. Our result shows that when adult preys are not showing anti-predator behavior, with an increase of maturation rate, the system exhibits a population cycle of abruptly increasing amplitude, which may drive all species of the system to extinction. Anti-predator sensitivity may exclude oscillation through homoclinic bifurcation and avert the prey population for any possible random extinction. Anti-predator sensitivity also decreases the predator population density and produces bistable dynamics. Higher values of anti-predator sensitivity may lead to the extinction of the predator population and benefit adult preys to persist with large population density. Below a threshold value of anti-predator sensitivity, it may possible to retain the predator population in the system by increasing the fear level of the predator. We also observe our fear-induced stage-structured model exhibits interesting and rich dynamical behaviors, various types of bistabilities in different bi-parameter planes. Finally, we discuss the potential impact of our findings.

在捕食者-猎物系统中，捕食者可以通过直接杀戮和（2）诱导捕食恐惧来影响猎物种群，最终迫使猎物采取一些反捕食者策略。然而，对于不同生命阶段的所有个体猎物，反捕食者的策略并不相同。此外，反捕食者行为既有成本也有收益，但大多数数学模型仅通过考虑其成本来观察动态。在本研究中，我们制定了一个捕食者-猎物模型，将猎物种群分为两个阶段：幼年和成年。我们假设成年猎物仅在对捕食敏感时才适应群体防御作为反捕食者策略。群体防御通过减少捕食对成年猎物起到积极作用，但在消极方面，它同时降低了它们的繁殖潜力。引入了一个参数，即反捕食者敏感性，将群体防御的收益和成本联系起来。我们的结果表明，当成年猎物没有表现出反捕食者行为时，随着成熟率的增加，系统表现出一个急剧增加的种群周期，这可能会导致系统的所有物种灭绝。反捕食者的敏感性可以通过同宿分叉排除振荡，并避免猎物种群发生任何可能的随机灭绝。反捕食者的敏感性也会降低捕食者的种群密度并产生双稳态动态。较高的反捕食者敏感性值可能会导致捕食者种群的灭绝，并有利于成年猎物以较大的种群密度持续存在。低于反捕食者敏感度的阈值，通过增加捕食者的恐惧程度，可以将捕食者种群保留在系统中。我们还观察到我们的恐惧诱导阶段结构模型表现出有趣且丰富的动态行为，不同双参数平面中的各种类型的双稳态。最后，我们讨论了我们发现的潜在影响。