基于大偏差理论的随机动力学研究

朱金杰; 陈朕; 孔琛; 刘先斌

doi:10.6052/1000-0992-18-021

基于大偏差理论的随机动力学研究

doi: 10.6052/1000-0992-18-021

朱金杰^1,2,†, ,,
陈朕^2,3,
孔琛^2,4,
刘先斌^2,*,

¹ 南京理工大学机械工程学院, 南京 210094
² 南京航空航天大学机械结构力学及控制国家重点实验室, 南京210016
³ 罗切斯特大学大脑与认知科学系, 美国罗切斯特 14627
⁴ 远景能源(江苏)有限公司数字化产品开发与应用部, 上海 200051

基金项目:

国家自然科学基金资助项目 (11772149, 11472126).

详细信息

作者简介:
朱金杰, 男, 1989年出生, 南京理工大学机械工程学院讲师.东京工业大学2020年JSPS博士后奖学金获得者,合作教授Hiroya Nakao. 本科毕业于南京航空航天大学工程力学钱伟长班. 研究生期间主要从事非线性随机动力学研究. 参与国家自然基金项目2项. 目前已在Physical Review E, Chaos, Proceedings of the Royal Society London A, Physics Letters A等期刊上发表SCI论文8篇, 其中第一作者6篇. 担任International Journal of Modern Physics B等期刊审稿人. 主要研究兴趣包括:复杂网络、神经元动力学、振动共振、大偏差理论等.|刘先斌, 男, 1965年出生,南京航空航天大学航空宇航学院教授, 博士生导师.主要从事非线性随机动力学:局部和全局随机分岔、噪声诱发混沌系统随机动力学行为、随机颤振、离出问题和随机共振等方面的研究.目前主持国家自然科学基金面上项目2项.已主持完成国家自然科学基金项目3项、教育部博士点基金和国家留学归国基金各1项、国家重点实验室基金项目2项.此外, 作为主要研究人员,参与完成国家自然科学基金重点项目、重大研究计划和面上项目4项. 已发表学术论文80余篇、论著1部. 论文发表在Proceedings of the Royal Society London A, ASME-Journal of Applied Mechanics,Physical Review E, Chaos, Nonlinear Dynamics,《力学学报》《中国科学》等国际、国内学术期刊,其中SCI检索期刊论文70余篇, 论文论著他引500篇次.

通讯作者:
朱金杰

刘先斌

中图分类号: O211.63
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出版历程
- 收稿日期: 2018-09-05
- 刊出日期: 2020-10-08

The researches on the stochastic dynamics based on the large deviation theory

ZHU Jinjie^{1,2,†
, ,},
CHEN Zhen^2,3,
KONG Chen^2,4,
LIU Xianbin^{2,*
,}

¹ School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China
² State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
³ Department of Brain and Cognitive Sciences, University of Rochester, Rochester 14627, United States
⁴ Department Digital Method and Product, Envision Energy, Shanghai 200051, China

More Information

Corresponding author: ZHU Jinjie; LIU Xianbin

摘要

摘要: 本文介绍了大偏差理论的基本思想、基本概念以及大偏差理论在离出问题研究中的应用.本文评述了有关离出问题的三个重要指标:平均首次离出时间、离出位置分布和最优离出路径相关研究的思路和方法,而其中对最优离出路径的刻化是结构性的难题. 针对平均首次离出时间,本文介绍了它与拟势的关系,并应用平均首次离出时间的结论分析了随机共振以及自诱导随机共振中的时间匹配机制.对于离出位置分布, 本文介绍了提高蒙特卡罗模拟速度的相关算法,并重点评述了其中的概率演化算法和相关的算例. 最后,对于最优离出路径的研究, 本文讨论了几类计算方法,分析了最优路径满足的辅助哈密尔顿系统轨线由于非线性多值性形成的拉格朗日流形拓扑结构的奇异性及其动力学含义,并进一步给出了有限噪声强度激励条件下的作用量修正方法. 最后,给出了大偏差理论应用发展的一些开放性问题的展望.
- 大偏差理论 /
- 离出问题 /
- 最优离出路径 /
- 平均首次离出时间 /
- 离出位置分布
Abstract: This paper introduces the basic ideas and concepts of large deviation theory and its application in the study of exit problems. Three critical indicators of exit problems are reviewed: mean first passage time, exit location distribution and most probable escape path. Among them, the characterization of the most probable escape path is a structural conundrum. For the mean first passage time, its relationship with quasi-potential is introduced, and it is applied to analyze the time matching mechanism in stochastic resonance and self-induced stochastic resonance. For the exit location distribution, the relevant algorithms to accelerate the Monte Carlo numerical simulation are discussed, and the probability evolution method is specially clarified with some interesting examples. For the study of the most probable escape path, several calculation methods are discussed, and the singularity of the topological structure and its dynamical implications of the Lagrangian manifold formed by the auxiliary Hamilton system trajectories are analyzed. Furthermore, the corrected action method under the condition of finite noise intensity is given. Finally, the prospect of some open problems for the application and development of large deviation theory is discussed.
- large deviation theory /
- exit problem /
- most probable escape path /
- mean first passage time /
- exit location distribution

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参考文献(154)

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