Department of Mathematics, National Institute of Technology Agartala, Jirania, West Tripura 799046, India.
Chaos. 2020 Jun;30(6):063129. doi: 10.1063/5.0006968.
The effect of induced fear in the prey due to the presence of a predator can alone develop anti-predator resistance to such an extent that it might reduce the prey reproduction in a significant amount. As fear can perceptibly affect the densities of the terrestrial vertebrates, here we investigate the cost of fear on a Holling type II predator-prey model associated with prey refuge and additional food to the predator. We evidently provide conditions on the existence and stability of equilibria as well as the occurrence of the Hopf bifurcation. Besides, we study how the presence of fear re-calibrates the effects of prey refuge and additional food in terms of quality and quantity on the system dynamics. We observe that the effect of fear not only reduces the predator density but also considerably drives the system toward stability. All the results presented here are mainly analytical but to make it more comprehensive, we perform numerical simulation. Moreover, to show the vast applicability of our results, we compare it with a few other models according to the presence of fear, refuge, and additional food.
由于捕食者的存在而导致猎物产生的恐惧效应，单独就可以使猎物产生足够的抗捕食者能力，从而显著减少猎物的繁殖量。由于恐惧可以明显影响陆生脊椎动物的密度，因此在这里，我们研究了恐惧对带有猎物避难所和额外食物的捕食者-猎物 Holling 型 II 模型的成本。我们显然提供了平衡点的存在和稳定性以及 Hopf 分支的发生的条件。此外，我们研究了恐惧的存在如何根据质量和数量重新调整猎物避难所和额外食物对系统动态的影响。我们观察到，恐惧的影响不仅降低了捕食者的密度，而且还极大地使系统趋于稳定。这里提出的所有结果主要是分析性的，但为了使其更全面，我们进行了数值模拟。此外，为了展示我们结果的广泛适用性，我们根据恐惧、避难所和额外食物的存在，将其与其他几个模型进行了比较。
