使用碎形-碎形衍生物对等性刺激性植物浮游生物物种进行数学建模
Sangeeta Kumawat1, Sanjay Bhatter1, Bhamini Bhatia1
1Department of Mathematics, Malaviya National Institute of Technology Jaipur, Jaipur, India.
Scientific reports
|August 28, 2024
概括
这项研究使用了一种新型的分数运算符来建模植物浮游生物的动态. 结果显示,增加的分数-分数参数可以加速模型的趋同,而不会影响平衡稳定性.
科学领域:
- 生态生态学 生态生态学
- 数学生物学 数学生物学
- 动态系统 动态系统
背景情况:
- 植物浮游生物的动态对于水生生态系统至关重要.
- 了解物种相互作用需要强大的数学模型.
- 分形微积分为复杂系统分析提供了先进的工具.
研究的目的:
- 通过使用一种新型的分数-分数运算符,研究相互作用的植物浮游生物物种模型的动态.
- 分析拟议模型的解决方案的存在,独特性和稳定性.
- 探索分数-分数参数对模型融合和稳定性的影响.
主要方法:
- 应用阿坦干纳-巴莱努分数-分数运算符的应用.
- 使用皮卡德-林德洛夫定理来证明存在和独特性.
- 平衡点的海尔斯-乌拉姆稳定性分析.
- 基于牛顿多项式的数值方案的开发.
主要成果:
- 这项研究证实了植物浮游生物模型的存在和解决方案的独特性.
- 确定了平衡点,并分析了它们的稳定性.
- 数字模拟证明了各种分数-分数顺序的动态行为.
- 长期记忆效应 (分数-分数顺序) 并没有显著改变平衡点稳定性.
结论:
- 分数-分数运算符为建模植物浮游生物动态提供了一个有价值的框架.
- 增加的分数-分数参数增加了趋同到平衡状态的速度.
- 该模型的稳定性是强大的长期记忆效应固有的分数-分数计算.
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