标题： 以捕食者-被捕食者模型中包含猎物群集行为和相互干扰的恐惧驱动的灭绝与(去)稳定化 显示英文标题

标题： Fear-driven extinction and (de)stabilization in a predator-prey model incorporating prey herd behavior and mutual interference

摘要： 一个确定性的两种物种捕食者-被捕食者模型，考虑了猎物的群体行为，以及相互干扰和恐惧效应。 我们提供了生物可行平衡点的动力学分析指南。 我们给出了在共存平衡点存在一些局部和全局分岔的条件。 我们还表明，恐惧可以导致猎物种群在有限时间内从共存区域中灭绝。 我们的数值模拟显示，通过适当选择参数来改变捕食者的恐惧强度，可以稳定和不稳定模型的共存平衡解。 此外，我们讨论了引入恒定捕获努力到捕食者种群对系统动态的影响，特别是从有限时间灭绝到稳定共存的变化。 此外，我们进行了广泛的数值实验以可视化模型的动力学行为并证实我们得到的结果。 显示英文摘要

摘要： A deterministic two-species predator-prey model with prey herd behavior is considered incorporating mutual interference and the effect of fear. We provide guidelines to the dynamical analysis of biologically feasible equilibrium points. We give conditions for the existence of some local and global bifurcations at the coexistence equilibrium. We also show that fear can induce extinction of the prey population from a coexistence zone in finite time. Our numerical simulations reveal that varying the strength of fear of predators with suitable choice of parameters can stabilize and destabilize the coexistence equilibrium solutions of the model. Additionally, we discuss the outcome of introducing a constant harvesting effort to the predator population in terms of changing the dynamics of the system, in particular, from finite time extinction to stable coexistence. Furthermore, we perform extensive numerical experiments to visualize the dynamical behavior of the model and substantiate the results we obtained.