李雅普诺夫指数与混沌系统参数敏感依赖性的联系
混沌动力学
2022-09-28 v3
摘要
混沌对参数的敏感依赖性是动力系统可积性与稳定性研究中的一个备受关注的话题。先前的工作已提出通过拓扑判据或大规模数值模拟来识别参数敏感依赖性的方法。在本文中，我们表明当系统的李雅普诺夫指数随参数变化而改变时，系统在对应于所考虑参数的轨道上呈指数发散。我们利用这一结果在不确定性区间内探讨对参数的敏感依赖性，并得出结论：该现象的刻画直接关联到我们为不同参数确定系统李雅普诺夫指数的能力。
引用
@article{arxiv.2208.09443,
title = {A connection between Lyapunov exponents and sensitive dependence on parameters of chaotic systems},
author = {Samuel Willian Schwertner Costiche and Carlos Henrique Coimbra-Araújo and Rodrigo André Schulz},
journal= {arXiv preprint arXiv:2208.09443},
year = {2022}
}
备注
We have received comments from reviewers of the article that point to a need for a complete rewording of the ideas exposed. We do not wish the content to negatively influence or serve as a reference for other research without a solid foundation