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Updated: May 25, 2025

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在Leslie-Gower捕食者-猎物模型中,具有Holling II功能响应和弱的Allee效应的更高密度的分叉
Zhenliang Zhu1, Qun Zhu2, Lingling Liu3
1School of Computer and Big Data, Minjiang Universit, Fuzhou, 350108, PR China.
捕食者-猎物模型中弱的Allee效应可以导致复杂的动态,包括更多的平衡和极限周期. 然而,高捕食率仍然会导致猎物灭绝和系统崩.
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.
- 霍林的II型功能反应描述了捕食者的食率.
- 基效应可以显著改变种群动态.
研究的目的:
- 为了分析一个莱斯利类型的掠食者-猎物系统与一个弱的艾利效应.
- 调查小效应对系统动态和分叉的影响.
- 探索导致猎物灭绝的条件.
主要方法:
- 对动态系统进行严格的数学分析.
- 分叉分析,包括尖端类型的无能和退化的霍夫分叉.
- 数字模拟使用MATCONT进行可视化.
主要成果:
- 该系统表现出复杂的分叉 (共维4和3).
- 弱的Allee效应增加了平衡的数量,并产生了多个极限周期.
- 高强度的掠食可能导致猎物灭绝和系统崩.
结论:
- 弱小效应丰富了捕食者-猎物系统的动态行为.
- 艾利效应和掠食之间的相互作用对生态系统的稳定性至关重要.
- 数学建模为生态现象提供了洞察力.
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