一类具有反捕食行为的修正的Leslie-Gower捕食者-食饵模型的动力学分析
Dynamic Analysis of a Modified Leslie-Gower Predator-Prey Model with Anti-Predation Behavior
DOI: 10.12677/AAM.2024.138354, PDF,   
作者: 安国生：西北师范大学数学与统计学院，甘肃 兰州
关键词: 反捕食行为；平衡点；稳定性；Hopf分支；跨临界分支；Anti-Predation Behavior； Equilibrium； Stability； Hopf Branch； Transcritical Bifurcation
摘要: 本文研究了一类具有反捕食行为的修正Leslie-Gower捕食者食饵模型，研究了加入反捕食行为对 模型动力学性态的影响，在新的常微分方程模型中，首先讨论了平衡点的存在性和稳定性，井以 b 作为分支参数讨论了Hopf分支的存在性和Hopf分支的方向和分支周期解的稳定性。 最后讨论了 跨临界分支。 研究表明反捕食行为可以有利于物种的共存平衡。
Abstract: In this paper, a modified Leslie-Gower predator prey model with anti-predator behav- ior is studied, and the effect of adding anti-predation behavior on the dynamics of the model is studied. In the new ordinary differential equation model, the existence and stability of the equilibrium point are first discussed, and the existence and Hopf of the Hopf branch are discussed with b as the branch parameter Direction of branch and stability of periodic solution of branch. Finally, the Transcritical branch is discussed. Studies have shown that anti-predation behavior can be beneficial to the coexistence balance of species.
文章引用：安国生. 一类具有反捕食行为的修正的Leslie-Gower捕食者-食饵模型的动力学分析[J]. 应用数学进展, 2024, 13(8): 3709-3721. https://doi.org/10.12677/AAM.2024.138354

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