具恐惧效应与趋避敏感性随机捕食模型动力学  

Dynamics of Stochastic Predator-Prey Model with Fear Effect and Predator-Taxis Sensitivity

作　　者：王欣琦 张天四[1] 

机构地区：[1]上海理工大学理学院,上海

出　　处：《理论数学》2022年第9期1399-1410,共12页Pure Mathematics

摘　　要：恐惧效应是捕食过程中的一种普遍反应,由食饵对捕食者的恐惧而产生的一系列自我保护行为。首先,通过构造一个合适的随机李雅普诺夫函数,给出了模型正解存在唯一平稳分布的充分条件;然后,通过对模型使用Itô’s公式,得到了模型中捕食者种群在两种情况下分别灭绝的充分条件。Fear effect is a common response in the process of predation, and the prey produces a series of self-protection behaviors because of its fear of predators. Firstly, a sufficient condition for the ex-istence and uniqueness of the ergodic stationary distribution of the positive solution of the model was given by a suitable stochastic Lyapunov function. Then, by using Itô’s formula to the model, the sufficient conditions for the extinction of predator population in the model were obtained in two cases.

关 键 词：捕食–食饵模型 恐惧效应 捕食者的趋避敏感性 平稳分布 遍历性 

分 类 号：Q141[生物学—生态学] O175[生物学—普通生物学]