具有时滞和恐惧效应的修正Leslie-Gower捕食–食饵模型的Hopf分岔研究
Hopf Bifurcation of a Modified Leslie-Gower Predator-Prey Model with Time Delay and Fear Effect
DOI: 10.12677/aam.2025.1410439, PDF,   
作者: 赵婉茹, 邱焕焕*：重庆交通大学数学与统计学院，重庆
关键词: 恐惧效应；时滞；修正Leslie-Gower；Hopf分岔；稳定性；Fear Effect； Delay； Modified Leslie-Gower； Hopf Bifurcation； Stability
摘要: 本文研究了一类具有恐惧效应和时滞的修正Leslie-Gower捕食–食饵模型，以时滞效应为分岔参数，系统分析了模型的Hopf分岔行为。首先讨论了系统正平衡点的稳定性和发生Hopf分岔的条件。其次利用中心流形定理和规范型理论，确定了Hopf分岔的方向以及周期解的稳定性。最后，通过数值模拟对理论结果进行验证。
Abstract: This paper studies a modified Leslie-Gower predator-prey model with fear effect and time delay, taking the time delay effect as the bifurcation parameter, and systematically analyzes the Hopf bifurcation behavior of the model. First, the stability of the positive equilibrium point and the conditions for Hopf bifurcation occurrence are discussed. Then, using the center manifold theorem and normal form theorem, the direction of Hopf bifurcation and the stability of periodic solutions are determined. Finally, numerical simulations are used to verify the theoretical results.
文章引用：赵婉茹, 邱焕焕. 具有时滞和恐惧效应的修正Leslie-Gower捕食–食饵模型的Hopf分岔研究[J]. 应用数学进展, 2025, 14(10): 269-280. https://doi.org/10.12677/aam.2025.1410439

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