具有恐惧效应的Filippov害虫-天敌模型的全局动力学
The Global Dynamics of the Filippov Pest-Natural Enemy Model with Fear Effect
DOI: 10.12677/AAM.2025.1410424, PDF,   
作者: 李土英：长沙理工大学数学与统计学院, 湖南 长沙；长沙理工大学工程数学建模与分析湖南省重点实验室, 湖南 长沙
关键词: Filippov系统；恐惧效应；平衡点；全局稳定性；Filippov System； Fear Effect； Equilibrium； Global Stability
摘要: 本文研究了一类具有恐惧效应的 Filippov 害虫-天敌模型, 应用 Filippov 方法研究了该模型的滑 模动力学, 并进一步研究了该模型的全局动力学, 证明了系统存在唯一的正平衡点, 且该平衡点是 全局渐近稳定的. 结果表明, 适当程度的恐惧效应能有效地把害虫数量控制阁值范围内, 避免害虫 数量爆发.
Abstract: In this paper, we investigate a class of Filippov pest-natural enemy model incorpo- rating a fear effect. The sliding mode dynamics of this model are studied using the Filippov approach, and further research is conducted on its global dynamics. It is proven that the system has a unique positive equilibrium, which is globally asymptot- ically stable. The results show that an appropriate degree of fear effect can effectively keep the number of pests within the control threshold and prevent the outbreak of pests.
文章引用：李土英. 具有恐惧效应的Filippov害虫-天敌模型的全局动力学[J]. 应用数学进展, 2025, 14(10): 100-114. https://doi.org/10.12677/AAM.2025.1410424

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