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一般化Ulam-Hyers-Rassias稳定性和新的可持续技术,用于动态分析全球变暖对生态系统的影响
Muhammad Farman1,2,3, Aamir Shehzad4, Kottakkaran Sooppy Nisar5
1Faculty of Arts and Science, Department of Mathematics, Near East University, Cyprus, Turkey. farmanlink@gmail.com.
Scientific reports
|December 17, 2023
概括
气候变化通过改变海洋条件对海洋生态系统产生影响. 本研究使用分数顺序模型来分析全球变暖下的鱼群动态和生态系统稳定性.
科学领域:
- 数学生物学 数学生物学
- 气候科学 气候科学
- 海洋学 海洋学 海洋学
背景情况:
- 气候变化导致海洋环境发生重大变化,影响温度,氧气和海洋酸化.
- 这些变化对海洋生态系统和依赖于它们的人类社会构成风险.
- 了解这些影响需要先进的建模技术.
研究的目的:
- 开发和分析气候变化下的水生生态系统的分数顺序数学模型.
- 研究全球变暖对鱼群动态和生态系统稳定的影响.
- 探索微积分计算对包含记忆效应的模型的影响.
主要方法:
- 使用Caputo分数运算符构建一个分数顺序模型,具有单数和非局部内核.
- 分析模型解决方案,鱼群的平衡状态,以及使用固定点定理的存在/独特性.
- 在系统稳定性分析中应用概括的乌兰-海尔斯-拉西亚斯函数.
- 使用两步拉格朗日多项式的计算模拟用于各种分数顺序和内核类型 (权力定律,指数,米塔格·莱弗勒).
主要成果:
- 该模型展示了积极不变的区域,确保了积极和有限的解决方案.
- 为鱼类种群发生和灭绝得出了平衡状态.
- 该研究强调了分数顺序对模型动态的显著影响,证明了记忆效应.
- 计算模拟可视化了分数顺序对不同模型组件的影响.
结论:
- 分数顺序建模为气候变化下的海洋生态系统复杂动态提供了宝贵的见解.
- 开发的模型和分析有助于更好地了解鱼群稳定性和灭绝风险.
- 这项研究建立了对渔业监督和海洋生态系统管理至关重要的数学联系.
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