在Ricker类型的掠食者-猎物模型中探索复杂的动态,并提供猎物避难所.
Ibraheem M Alsulami1, Rizwan Ahmed2, Faraha Ashraf3
1Mathematics Department, Faculty of Science, Umm Al-Qura University, Makkah 21955, Saudi Arabia.
Chaos (Woodbury, N.Y.)
|February 3, 2025
概括
猎物避难所稳定了捕食者-猎物模式,增强了生态系统的弹性. 本研究分析了离散时间模型中的固定点和分叉点,证实了避难所的存在.
科学领域:
- 生态动力学 生态动力学
- 数学生物学的数学生物学
- 非线性动力学是一种非线性动力学.
背景情况:
- 捕食者-猎物模型是生态学的基础.
- 离散时间模型为人口波动提供了洞察力.
- 猎物避难所是影响人口稳定的关键因素.
研究的目的:
- 研究猎物避难所对离散时间捕食者-猎物模型的影响.
- 分析模型固定点的稳定性.
- 探索使用二叉理论的分叉 (周期加倍和尼马克-萨克) .
主要方法:
- 固定点及其稳定性的分析.
- 中心多重体理论的应用.
- 利用分叉理论来研究动态过渡.
- 数字模拟用于验证.
主要成果:
- 对固定点的存在和稳定性进行了彻底的研究.
- 确定和分析了周期翻倍和尼马克-萨克分叉.
- 数字模拟证实了理论发现.
- 猎物避难所对模型表现出显著的稳定效应.
结论:
- 整合猎物避难所可以提高捕食者-猎物系统的稳定性和弹性.
- 离散时间模型与避难所提供了一个更现实的生态框架.
- 两叉分析揭示了受避难所影响的复杂动态.
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