这些转换保留了洛伦兹类系统的微分形式的独特性
Claudia Lainscsek1,2, Eduardo M A M Mendes3, Gustavo H O Salgado4
1Computational Neurobiology Laboratory, The Salk Institute for Biological Studies, 10010 North Torrey Pines Road, La Jolla, California 92037, USA.
Chaos (Woodbury, N.Y.)
|October 13, 2023
概括
多个普通微分方程可以产生相同的动态系统行为. 这项研究表明,不同的洛伦兹类系统共享相同的冲动形式也共享时间序列数据,揭示了动态系统建模中的非独特性.
科学领域:
- 动态系统 动态系统
- 数学物理 数学物理
- 混沌理论 混沌理论
背景情况:
- 普通微分方程对于建模物理系统至关重要.
- 对于动态系统的微分方程模型的独特性经常被假定,但并不总是真实的.
- 转换为或微分形式是一种用于分析动态系统的技术.
研究的目的:
- 为了研究微分方程的独特性,当转换成动形式时.
- 为了确定是否代数不同的系统可以共享相同的冲动形式和时间序列.
- 分析一组17个洛伦兹类系统的共享形和时间序列.
主要方法:
- 将3D普通微分方程转换为动形式.
- 分析转化后形和时间序列的保存情况.
- 对比17个代数上不同的洛伦兹式系统,具有相同的功能动形式.
- 基于共享的 jerk 参数的分组系统.
主要成果:
- 在转换中保留了动形式,这意味着转换后的系统共享了原始系统的变量的时间序列.
- 多个不同代数的普通微分方程系统可以共享相同的动形式.
- 系统共享相同的动形式也可以共享相同的时间序列转换变量,取决于动形式参数.
- 一组由17个洛伦兹类系统组成的小组展示了共享的功能动形式,并在子组中共享动参数和时间序列.
结论:
- 动态系统的微分方程模型并不总是独一无二的.
- 形转换保留了特定变量的时间序列.
- 在代数上不同的系统可以在共享相同的形和参数时表现出相同的动态行为.
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