一类具有Holling Ⅱ型功能反应及庇护效应的捕食-食饵生态流行病模型的动力学分析
Dynamic Analysis of a Predator-Prey Ecological Epidemic Model with Holling Ⅱ Functional Response and Shelter Effect
王立阳 1罗颜涛 1余庆2
作者信息
- 1. 新疆大学数学与系统科学学院,新疆乌鲁木齐 830017
- 2. 西南计算机有限责任公司,重庆 400060
- 折叠
摘要
为研究食饵庇护效应和捕捞如何综合影响生态系统的动态行为,提出一类具有捕捞项、食饵庇护效应以及Holling Ⅱ功能反应函数的捕食-食饵生态流行病模型.在可行域上得到模型解的正性和一致有界性,并给出模型的基本阈值动力学,随后借助Hurwitz判据,Dulac准则以及Lyapunov函数分别讨论系统各平衡点的局部渐近稳定性和全局稳定性.结果表明捕捞是影响食饵种群疾病灭绝的重要因素,同时对捕食者种群数量的增长也有一定的影响.
Abstract
To investigate the combined effects of prey refuge and fishing on the dynamic behavior of ecosystems,a predator-prey eco-epidemiological model with fishing terms,prey refuge effect,and Holling Ⅱ functional re-sponse function is proposed.The positivity and uniform boundedness of the model's solution on the feasible do-main are obtained,and the basic threshold dynamics of the model are presented.Subsequently,the local asymptot-ic stability and global stability of each equilibrium point of the system are discussed using Hurwitz criterion,Du-lac criterion,and Lyapunov function,respectively.The results indicate that fishing is a crucial factor affecting the extinction of diseases in prey populations,and it also has a certain impact on the growth of predator populations.
关键词
生态流行病模型/稳定性/Holling/Ⅱ反应函数/捕捞/庇护效应Key words
ecological epidemic model/stability/Holling Ⅱ reaction function/fishing/shelter effect引用本文复制引用
出版年
2024
NETL
NSTL
万方数据