随机扰动动态系统的稳定和不稳定多元体的数值计算:操作员的方法
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Experimental Methods to Study Human Postural Control
Published on: September 11, 2019
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Kaio C B Benedetti1, Paulo B Gonçalves2, Stefano Lenci3
1School of Civil and Environmental Engineering, Federal University of Goiás, Goiânia, Brazil.
Chaos (Woodbury, N.Y.)
|March 11, 2026
概括
非线性动态系统中的不变多元体是使用可测量动力学理论对非确定性系统进行概括的. 这项研究定义并证明了它们的存在,提供了计算方法,并揭示了微型架构中的随机现象.
科学领域:
- 动态系统理论 动态系统理论
- 随机过程 随机过程
- 几何动力学 几何动力学
背景情况:
- 不变变种群对于理解非线性动态系统的长期行为至关重要.
- 将不变多元体泛化为非确定性系统需要考虑概率行为和不确定性.
- 可测量的动力学理论提供了必要的工具,如转移运算符和乌拉姆离散.
研究的目的:
- 定义和确定不确定性的动态系统不变的多样性的存在.
- 开发一个计算框架,用可测量的动态来分析这些多元体.
- 调查随机现象对多重行为的影响.
主要方法:
- 从可测量的动态中利用概念,包括流量图和转移运算符 (在封闭和开放空间中的双重运算符).
- 应用了Ulam离散式到常量分布的空间.
- 定义并证明了不稳定的多元分布 (fWu) 和稳定的多元可观 (gWs) 的存在.
主要成果:
- 确立了fWu存在于不稳定的多重体上,其双可观察的gWs存在于稳定的多重体上.
- 为计算fWu和gWs的开放流转移运营商提出了一个离散化策略.
- 观察到在电力驱动的微架中趋同概率降低,稳定的多元体扩张和不稳定的多元体融合.
结论:
- 可测量的动力学理论成功地定义并证明了不稳定的多元分布和稳定的多元可观测的存在.
- 介绍了一种基于开放流转移运算符的Ulam离散的计算方法.
- 该研究揭示了相互关联的随机现象,影响系统动态和多重结构.
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