具有Michaelis-Menten型离散捕食者–猎物模型的分岔分析
Bifurcation Analysis of Discrete Predator-Prey Model with Michaelis-Menten Type
DOI: 10.12677/aam.2025.141036, PDF,    国家自然科学基金支持
作者: 王秀叶, 李自尊, 姚庆娟：南宁师范大学数学与统计学院，广西 南宁
关键词: Michaelis-Menten型；离散时间；倍周期分岔；Neimark-Sacker分岔；Michaelis-Menten Type； Discrete Time； Period-Doubling Bifurcation； Neimark-Sacker Bifurcation
摘要: 本文研究了捕食者具有Michaelis-Menten型离散捕食者–猎物模型的动力学问题。为了探索模型的丰富动力学性质，采用欧拉近似得到离散时间的Leslie-Gower模型。给出了内部不动点的存在性及其局部渐近稳定性。在此基础上，利用分岔理论和中心流形定理，研究了倍周期分岔和Neimark-Sacker分岔。并取临界参数进行数值模拟，验证了倍周期分岔和Neimark-Sacker分岔的存在性。
Abstract: In this paper, we investigate the dynamics of predator with Michaelis-Menten discrete predator-prey model. In order to explore the rich dynamic properties of the model, the discrete-time Leslie-Gower model is obtained by using Euler approximation. The existence of internal fixed points and their local asymptotic stability are given. On this basis, using bifurcation theory and central manifold theorem, the period-doubling bifurcation and Neimark-Sacker bifurcation are studied. The existence of period-doubling bifurcation and Neimark-Sacker bifurcation is verified by numerical simulation with critical parameters.
文章引用：王秀叶, 李自尊, 姚庆娟. 具有Michaelis-Menten型离散捕食者–猎物模型的分岔分析[J]. 应用数学进展, 2025, 14(1): 360-373. https://doi.org/10.12677/aam.2025.141036

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