结合Allee效应的植物-草食动物模型的动力学和控制
Muhammad Qurban1, Abdul Khaliq1, Kottakkaran Scooppy Nisar2
1Department of Mathematics, Riphah International University, Lahore, Pakistan.
Heliyon
|June 3, 2024
概括
这项研究使用离散时间植物-食草动物模型模拟了葡萄和葡萄藤相互作用. 国家反混乱控制有效地管理人口波动和不可预测的动态.
科学领域:
- 生态生态学 生态生态学
- 数学生物学 数学生物学
- 系统动力学 系统动力学
背景情况:
- 葡萄藤和葡萄的相互作用对于农业害虫管理至关重要.
- 盟友的效应和捕食者的功能反应显著影响着种群动态.
- 离散时间模型对于理解生态系统稳定性至关重要.
研究的目的:
- 分析一个离散时间植物-食草动物模型的定性行为,结合Allee的效应和捕食者反应.
- 为了研究在平衡点上的分叉和稳定性.
- 探索状态反混沌控制,以管理人口动态.
主要方法:
- 开发一个二维离散时间植物-食草动物模型.
- 应用线性稳定性理论和分叉分析 (尼马克-萨克,超临界).
- 使用数值模拟实现和验证状态反混乱控制.
主要成果:
- 对模型的边界和内部固定点的识别.
- 在边界平衡处证明一个跨临界分叉,在正稳定状态处证明一个尼马克-萨克分叉.
- 验证混沌控制在稳定人口动态方面的有效性.
结论:
- 离散时间植物-食草动物模型表现出复杂的动态,包括分叉.
- 国家反混沌控制是管理葡萄树和葡萄树种群的可行策略.
- 该研究通过数学建模提供了对生态稳定性和害虫防治的见解.
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