捕食者患病的捕食–食饵模型的定性分析
Qualitative Analysis of Predator-Prey Model with Infected Disease in Predator
DOI: 10.12677/AAM.2021.109320, PDF,  被引量    科研立项经费支持
作者: 李 敏, 卢 旸*：东北石油大学数学与统计学院应用数学系，黑龙江 大庆
关键词: 捕食–食饵模型；全局稳定性；捕食者患病；一致持久性；定性分析；Predator-Prey Model； Global Stability； Infected Predator； Uniform Persistence； Qualitative Analysis
摘要: 本文研究了捕食者患病的捕食–食饵模型，文中假设疾病仅在捕食者之间流行，其中易感捕食者和患病捕食者都具有捕获食饵的能力。本文首先运用极限理论以及构造Lyapunov函数的方法分别得到了各个边界平衡点的全局稳定性；其次运用一致持久生存理论得到了患病捕食者一致持久生存的充分条件。最后，运用数值模拟验证并补充了定性理论分析的结果。
Abstract: In this paper, we study a predator-prey model with infected disease for predator. It is assumed that the disease only spreads among predators, both susceptible predators and infected predators have the ability to catch preys. Firstly, the global stability of each boundary equilibrium point is obtained by using the limit theory and the method of constructing the Lyapunov function. Secondly, we get the sufficient conditions of uniform persistence for the infected predator by using the uniform persistence theory. Finally, numerical simulation verifies and complements the results of qualitative theoretical analysis.
文章引用：李敏, 卢旸. 捕食者患病的捕食–食饵模型的定性分析[J]. 应用数学进展, 2021, 10(9): 3059-3074. https://doi.org/10.12677/AAM.2021.109320

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