具有等比例的猎物避难所的Holling I型捕食-食饵模型的全局动力学
Global Dynamics of Holling Type I Predator-Prey Model with Equal Proportion of Prey Refuge
DOI: 10.12677/PM.2023.134096, PDF, HTML, 下载: 232  浏览: 327 
作者: 罗 丹：长沙理工大学数学与统计学院，湖南 长沙
关键词: 非光滑系统；捕食-食饵模型；不连续；平衡点；稳定性；Non-Smooth System； Predator-Prey Model； Discontinuous； Equilibrium； Stability
摘要: 在本文中，通过引入阈值策略，研究一类具有等比例的猎物避难所的Holling I型捕食-食饵模型并对其进行了全局分析，以确定模型的全局动力学。 现利用Filippov 理论，Lyapunov 函数法和格林公式等方法，在两个子系统的全局动力学的基础上，对阈值策略下的捕食-食饵模型，我们研究其滑模动力学和全局动力学。 最后通过数值模拟对理论结果进行验证。
Abstract: In this paper, The objective of this paper is to investigate a Global dynamics of Holling type I predator-prey model with equal proportion of prey refuge by introducing threshold strategy. Here we provide a global qualitative analysis to determine the global dynamics of the model. Making use of Filippov theory, Lyapunov functions and Green formula, on the basis of global dynamics of two subsystems, for the predator-prey model under threshold strategy, we examine the sliding mode dynamics and the global dynamics. Finally, the theoretical results are verified by numerical simulation.
文章引用：罗丹. 具有等比例的猎物避难所的Holling I型捕食-食饵模型的全局动力学[J]. 理论数学, 2023, 13(4): 902-916. https://doi.org/10.12677/PM.2023.134096

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