修改的莱斯利-高尔捕食者-猎物模型的动力学与双重的艾利效应
Mengyun Xing1, Mengxin He2, Zhong Li1
1School of Mathematics and Statistics, Fuzhou University, Fuzhou 350108, China.
Mathematical biosciences and engineering : MBE
|February 2, 2024
概括
这项研究探讨了与Allee效应的捕食者-猎物模型,揭示了复杂的动态. 修改后的莱斯利-高尔模型表现出多个平衡和丰富的分叉,包括博格达诺夫-塔肯斯和退化的霍夫分叉.
科学领域:
- 生态生态学 生态生态学
- 数学生物学 数学生物学
- 动态系统 动态系统
背景情况:
- 捕食者-猎物模型是生态学的基础.
- 莱斯利-高尔模型是捕食者-猎物动态的一个经典框架.
- 纳入Allee效应,它降低了低人口密度的人均增长率,增加了生态模型的复杂性.
研究的目的:
- 为了研究改造的莱斯利-高尔捕食者-猎物模型的动态行为.
- 分析Allee效应对猎物和捕食者种群的影响.
- 在模型中识别和描述两叉和平衡点.
主要方法:
- 微分方程的数学建模和分析.
- 对平衡点及其稳定性的分析.
- 调查局部和全球分叉,包括结,霍夫和博格达诺夫-塔肯斯分叉.
主要成果:
- 该模型最多有两个正平衡.
- 一个平衡是一个夸张的,而另一个是弱焦点,多重性至少为三.
- 该系统表现出三次元的顶点,并经历博格达诺夫-塔肯斯和退化的霍夫分叉,导致两个极限周期.
结论:
- 与更简单的模型相比,经过修改的Leslie-Gower模型具有双重Allee效应,显示了显著丰富的动态.
- 分叉分析揭示了复杂的现象,如退化的霍夫分叉和多个极限周期.
- 这些发现有助于更深入地了解在具有挑战性的环境条件下人口动态.
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