骨矿化非线性微分动态系统的数值和图形模拟
Ritu Agarwal1, Pooja Airan1, Mohammad Sajid2
1Department of Mathematics, Malaviya National Institute of Technology, Jaipur 302017, India.
Mathematical biosciences and engineering : MBE
|June 14, 2024
概括
这项研究使用微积分计算来模拟骨矿化,为这个复杂的生物过程提供了新的见解. 数学分析和模拟揭示了分数运算符在捕获骨动态方面的有效性.
科学领域:
- 生物数学是生物数学.
- 计算生物学 计算生物学
- 分数微积分的计算.
背景情况:
- 骨矿化是一种复杂的生物过程,对骨健康至关重要.
- 现有的模型可能无法完全捕捉骨形成和重塑的复杂动态.
- 分数计算为模拟具有内存效应的复杂系统提供了一个强大的框架.
研究的目的:
- 为了更好地理解Komarova的骨矿化模型,使用卡普托-法布里齐奥分数运算符.
- 在分数模型中分析解决方案的边界性,存在,独特性和稳定性.
- 通过敏感性分析研究模型参数对系统行为的影响.
主要方法:
- 使用卡普托-法布里齐奥分数运算符进行数学建模.
- 对溶液属性的分析,包括边界性,存在性,独特性和稳定性.
- 灵敏度分析以评估参数的影响.
- 使用分数亚当斯-巴斯福斯方法进行数值和图形模拟.
主要成果:
- 这项研究提供了一个全面的数学框架,用于骨矿化使用分数计算.
- 分析证实了在拟议的分数模型中的解决方案的存在,独特性和稳定性.
- 灵敏度分析确定了影响骨矿化过程的关键参数.
- 数字模拟表明模型能够表示复杂的动态.
结论:
- 分数计算,特别是卡普托-法布里齐奥运算子,为模拟骨矿化提供了有价值的工具.
- 与整数顺序模型相比,分数模型提供了新的见解,突出显示了记忆效应的重要性.
- 这种方法提高了我们对骨健康和疾病背后的复杂生物机制的理解.
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