具有恒定容量避难所的 Filippov捕食者-食饵模型的全局动力学
Global Dynamics of a Filippov Predator-Prey Model with a Constant-Capacity Refuge
DOI: 10.12677/AAM.2023.123123, PDF, HTML, 下载: 254  浏览: 335 
作者: 蒋 杉, 周 培：长沙理工大学数学与统计学院，湖南 长沙
关键词: 捕食者-食饵系统；避难所；平衡点；稳定性；Predator-Prey Model； Refuge； Equilibrium； Stability
摘要: 本文研究了一类具有恒定容量避难所的Filippov捕食者-食饵模型。 应用Filippov方法研究了模型的滑模动力学，并进一步研究了模型的全局动力学。 证明了系统存在唯一的正平衡，且该平衡是 全局渐近稳定的。结果表明，建立适当容量的避难所有利于维持捕食者与被捕食者之间的平衡。
Abstract: In this paper, a predator-prey model with a constant-capacity refuge is studied. We apply Filippov method to study the sliding mode dynamics of the model, and studied the global dynamics furtherly. It is proved that there exists a unique equilibrium and the equilibrium is globally asymptotically stable. The results show that the estab- lishment of a refuge with appropriate capacity is beneficial to maintain the balance between predator and prey.
文章引用：蒋杉, 周培. 具有恒定容量避难所的 Filippov捕食者-食饵模型的全局动力学[J]. 应用数学进展, 2023, 12(3): 1215-1223. https://doi.org/10.12677/AAM.2023.123123

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