一个理论和计算动态分析由于长期存在内部排放的有毒物质而导致变形的生物群体
Digvijai Singh1, Joydip Dhar2, Alok Kumar Agrawal1
1Department of Mathematics, Amity School of Applied Sciences, Amity University, Lucknow Campus, Lucknow, Uttar Pradesh, 226010, India.
MethodsX
|April 17, 2025
概括
有毒物质会带来异常的生物变化,延迟,影响物种的生存. 这项研究模拟了这些延迟,以了解人口动态,并找到对环境毒素的最佳控制策略.
科学领域:
- 生态生态学 生态生态学
- 数学生物学 数学生物学
- 环境科学 环境科学
背景情况:
- 废物和工业化的环境毒素导致生物物种发生异常变化.
- 这些毒剂诱导的变化以显著的延迟表现,使物种生存和种群动态复杂化.
- 现有的模型往往不能完全考虑与毒性影响相关的时间延迟.
研究的目的:
- 开发和分析生物种群的数学模型,包括延迟变形和毒性物质耗尽.
- 调查这些延迟对人口稳定和Hopf分叉的潜在影响.
- 确定最佳的控制策略,以减轻内部排放的有毒物质的影响.
主要方法:
- 开发一个变形的生物种群模型,具有种群变形延迟和毒性物质耗尽延迟.
- 使用数学技术分析系统稳定性和Hopf分叉.
- 应用最佳控制理论和庞特里亚金的最大原则来最大限度地降低控制成本.
- 使用MATLAB进行数值模拟以验证理论发现.
主要成果:
- 确定了影响系统稳定性的变形和耗尽延迟的关键值.
- 证明了霍夫分叉的发生,表明复杂的动态行为.
- 制定了具有成本效益的控制策略,以管理对人口的有毒物质影响.
- 通过数值模拟验证模型的预测.
结论:
- 种群变形和有毒物质耗尽延迟显著影响生物种群动态和稳定性.
- 开发的模型提供了关于毒素,延迟和人口健康之间的复杂相互作用的见解.
- 可以有效地使用最佳控制策略来减轻环境毒素的不良影响.
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