具有避难所的不连续食饵–捕食者模型的动力学研究
Dynamics Research of a Discontinuous Predator-Prey Model with Shelter
DOI: 10.12677/AAM.2022.115322, PDF,   
作者: 张 芸：长沙理工大学数学与统计学院，湖南 长沙
关键词: 食饵–捕食者模型；Lyapunov函数；平衡点；稳定性；Predator-Prey Model； Lyapunov Function； Equilibrium； Stability
摘要: 本文研究了一类基于避难所控制策略的不连续食饵–捕食者模型的全局动力学。利用Filippov理论和非光滑分析方法得到了实平衡点和伪平衡点的存在性，并证明了这些平衡点的全局渐近稳定性。借助数值模拟，分析了所得结果的生物学意义。
Abstract: In this paper, the global dynamics of a discontinuous predator-prey model based on shelter control strategy is studied. By using Filippov theory and non-smooth analysis method, the existence of real equilibrium and pseudo equilibrium is obtained, and the global asymptotic stability of these equi-libria is proved. With the help of numerical simulation, the biological significance of the obtained results is analyzed.
文章引用：张芸. 具有避难所的不连续食饵–捕食者模型的动力学研究[J]. 应用数学进展, 2022, 11(5): 3028-3034. https://doi.org/10.12677/AAM.2022.115322

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