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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

朱金杰, 陈朕, 孔琛, 刘先斌. 基于大偏差理论的随机动力学研究[J]. 力学进展, 2020, 50(1): 202010. doi: 10.6052/1000-0992-18-021
引用本文: 朱金杰, 陈朕, 孔琛, 刘先斌. 基于大偏差理论的随机动力学研究[J]. 力学进展, 2020, 50(1): 202010. doi: 10.6052/1000-0992-18-021
ZHU Jinjie, CHEN Zhen, KONG Chen, LIU Xianbin. The researches on the stochastic dynamics based on the large deviation theory[J]. Advances in Mechanics, 2020, 50(1): 202010. doi: 10.6052/1000-0992-18-021
Citation: ZHU Jinjie, CHEN Zhen, KONG Chen, LIU Xianbin. The researches on the stochastic dynamics based on the large deviation theory[J]. Advances in Mechanics, 2020, 50(1): 202010. 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
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

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

More Information
    Corresponding author: ZHU Jinjie; LIU Xianbin
  • 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.

     

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  • 收稿日期:  2018-09-05
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