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两维离散时间生物模型的动力学和控制,包括弱的Allee效应
Muhammad Qurban1, Abdul Khaliq1, Muhammad Saqib2
1Department of Mathematics, Riphah International University, 54660 Lahore, Pakistan.
Chaos (Woodbury, N.Y.)
|September 3, 2024
概括
这项研究分析了一个离散时间的掠食者-猎物模型,具有弱的Allee效应,揭示了复杂的动态和混乱. 混沌控制策略是通过模拟提出和验证的.
科学领域:
- 人口动态 人口动态
- 数学生物学 数学生物学
- 非线性动力学是一种非线性动力学.
背景情况:
- 离散时间模型提供了比连续模型更丰富的动态,经常表现出混乱.
- 阿利效应描述了低人口密度的人均增长的减少,影响了人口的生存能力.
- 了解捕食者与猎物的相互作用对于生态稳定和管理至关重要.
研究的目的:
- 为了研究一个离散时间捕食者-猎物模型中的非线性稳定性和分叉,具有弱的Allee效应.
- 分析Allee效应对猎物种群动态和整体系统稳定性的影响.
- 为这个生态模型开发和验证混乱控制策略.
主要方法:
- 两叉理论,包括中心多样数定理和Ljapunov-Schmidt还原.
- 正常形式理论和普遍展开,用于分析稳定性.
- 稳定理论和固定点的拓分类.
- 数字模拟用于验证理论发现和混乱控制.
主要成果:
- 该模型展示了边界固定点 (A1,A2) 和一个唯一的正固定点 (A*).
- 在A2发生翻转分叉,在A*附近发生尼马克-萨克分叉.
- 与连续模型相比,离散时间模型显示了高度混乱的行为.
- 建议的混乱控制策略 (状态反,混合) 有效地管理系统动态.
结论:
- 弱的Allee效应显著影响了猎物动态,并可能导致在离散的捕食者-猎物系统中出现复杂,混乱的行为.
- 两叉分析为稳定性过渡和混乱的潜力提供了关键的见解.
- 可以使用有效的混乱控制方法来稳定这些复杂的生态模型.
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