The main object of this work is to analyse the impacts of fear effect on the dynamics of predator–prey interaction incorporating non linear prey refuge to control the extinction of predator. We have taken a Holling type II functional response in presence of additional food. The positivity and uniform boundedness of solutions have been discussed. The feasibility conditions of all equilibrium points and their stability behaviours are derived. Next, we have studied the existence of local bifurcation (transcritical bifurcation) of codimension 1. Moreover, impacts of fear effect have been studied analytically and noticed that the predator biomass can not only be decreased at the interior equilibrium by the effect of fear but the system also be stabilized by excluding the existence of periodic solutions through Hopf-bifurcation. In addition, uniform persistence of our proposed system has been discussed analytically. Further, we have analysed the stability behaviours of the interior eq...

中文翻译：

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在恐惧效应和额外食物的影响下，带有非线性猎物避难所的捕食者与猎物相互作用的延迟动力学

这项工作的主要目的是分析恐惧效应对结合非线性猎物避难所控制捕食者灭绝的捕食者与猎物相互作用动力学的影响。我们在有其他食物的情况下进行了Holling II型功能性反应。讨论了溶液的正性和一致有界性。推导了所有平衡点的可行性条件及其稳定性。接下来，我们研究了余维1的局部分支（跨临界分支）的存在。此外，通过分析研究了恐惧效应的影响，并注意到捕食者的生物量不仅可以通过恐惧效应在内部平衡时减少，而且可以通过排除存在Hopf分支的周期解，也可以稳定系统。此外，我们提出的系统的统一持久性已通过分析进行了讨论。此外，我们分析了内部方程的稳定性行为。