带有恐惧的捕食者染病的捕食系统的动力学研究
Dynamics Research of Predator-Prey System with Fear and Disease in Predators

最近对于脊椎动物的野外实验表明，仅是捕食者的存在就会引起猎物种群数量的巨大变化。猎物因捕食者存在而产生的恐惧会影响到猎物自身的繁殖。基于实验结果，我们提出了一个考虑恐惧效应和捕食者染病的捕食模型。本文我们提出了一个三物种的食物链模型，由于捕食者物种内有传染病，所以将捕食者分为染病捕食者和易感捕食者,且传染病会削弱捕食者的捕食能力。我们研究了平衡点的所有性质，建立了模型局部稳定的条件。利用李雅普诺夫函数来研究平衡点的全局稳定性，并研究了局部分岔分析。
Recent field experiments on vertebrates have shown that merely the presence of predators can cause significant changes in the population size of prey. The fear of predators in prey can affect their own reproduction. Based on the experimental results, we proposed a predator-prey model considering the fear effect and the disease of predators. In this paper, we present a three-species food chain model. Since there is an infectious disease within the predator species, the predators are divided into infected predators and susceptible predators, and the disease weakens the predation ability of the predators. We studied all the properties of the equilibrium points and established the conditions for local stability of the model. The global stability of the equilibrium points was studied using the Lyapunov function, and the local bifurcation analysis was also conducted.