在使用克劳利-马丁功能反应的猎物-掠食者-掠食者模型中,周期翻倍级联到混乱和最佳的二次收获
Rajalakshmi Manoharan1, Reenu Rani2, Manpreet Kaur3
1Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu, 632014, India.
Scientific reports
|August 29, 2025
概括
这项研究引入了捕食掠食者掠食者模型,揭示了包括混乱和分叉在内的复杂动态. 建议采用最佳收获策略,以平衡收入和人口管理.
科学领域:
- 生态学
- 数学生物学
- 理论生态学
背景情况:
- 生态模型对于理解物种相互作用至关重要.
- 捕捞对人口动态和生态系统稳定性产生重大影响.
- 克劳利-马丁功能反应模型捕食者-猎物相互作用.
研究的目的:
- 提出和分析一个捕食者-掠食者-掠食者模型.
- 研究复杂的动态行为,包括混乱和分叉.
- 确定可持续管理的最佳采集策略.
主要方法:
- 生态系统的数学建模.
- 对平衡点及其稳定性的分析.
- 对分叉的研究 (跨临界,Hopf,一般化的Hopf).
- 应用Pontryagin的最大原则以实现最佳控制.
- 数字模拟 (时间序列,相位图,分叉图).
主要成果:
- 建立模型的积极性和有限性.
- 确定可行的平衡点及其稳定条件.
- 观察到极限周期,周期翻倍的混乱路线,以及各种分叉.
- 为了保持均的条件.
- 描述了经济和生态平衡的最佳收获控制.
结论:
- 该模型表现出丰富的动态,包括混乱的行为和分叉,在二次收获下.
- 最佳的控制策略可以有效地管理收获力度以获得可持续的产量.
- 数学建模为生态管理和保护提供了宝贵的见解.
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