具有Beddington-DeAngelis型功能反应函数的阶段结构捕食-食饵模型  

Stage-Structured Predator-Prey Model with Beddington-DeAngelis Type Functional Response Function

作　　者：卢旸 李敏 LU Yang;LI Min(Department of Applied Mathematics,College of Mathematics and Statistics,Northeast Petroleum University,Daqing 163000,China)

机构地区：[1]东北石油大学数学与统计学院应用数学系,黑龙江工大庆163000

出　　处：《数学的实践与认识》2022年第11期263-275,共13页Mathematics in Practice and Theory

基　　金：东北石油大学人才引进科研启动经费项目(1305021838)。

摘　　要：讨论了捕食者和食饵都具有阶段结构的捕食食饵模型.考虑到捕食者梭皮龟捕获食饵水母时彼此之间的干扰效应,用到了Beddington-DeAngelis型功能反应函数,食饵水母的幼年为水螅体,捕食者梭皮龟仅以成年水母为食.运用渐近系统理论得到了模型边界平衡点的全局渐近稳定性,运用一致持久生存理论得到了捕食者的一致持久性.最后,运用数值模拟的方式不仅验证了定性理论分析的结果,同时显示了捕食者之间适当的干扰可以有效控制水母种群的数量.In this paper,a predator-prey model with stage structure for both the predator and the prey is investigated.We consider the interference effect between predator leatherback turtle when they catch the prey jellyfish,and we use the Beddington-DeAngelis functional response function.The juvenile of the prey jellyfish is the polyp,and predator leatherback turtle only feeds on the adult jellyfish.The global asymptotic stability of the boundary equilibrium point is obtained by using the asymptotic system theory,and the uniform persistence of the predator is obtained by using the theory of uniform persistence.Finally,the numerical simulation not only verifies the results of qualitative theoretical analysis,but also shows that appropriate interference among predators can control the jellyfish population effectively.

关 键 词：捕食食饵模型 阶段结构 Beddington-DeAngelis型功能反应 全局稳定性 一致持久性 

分 类 号：O175[理学—数学] Q141[理学—基础数学]