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Quasi-Potential Calculation and Minimum Action Method for Limit Cycle
Lin, Ling1; Yu, Haijun2,3,4; Zhou, Xiang5,6
2019-06-01
Source PublicationJOURNAL OF NONLINEAR SCIENCE
ISSN0938-8974
Volume29Issue:3Pages:961-991
AbstractWe study the noise-induced escape from a stable limit cycle of a non-gradient dynamical system driven by a small additive noise. The fact that the optimal transition path in this case is infinitely long imposes a severe numerical challenge to resolve it in the minimum action method. We first consider the landscape of the quasi-potential near the limit cycle, which characterizes the minimal cost of the noise to drive the system far away form the limit cycle. We derive and compute the quadratic approximation of this quasi-potential near the limit cycle in the form of a positive definite solution to a matrix-valued periodic Riccati differential equation on the limit cycle. We then combine this local approximation in the neighborhood of the limit cycle with the minimum action method applied outside of the neighborhood. The neighborhood size is selected to be compatible with the path discretization error. By several numerical examples, we show that this strategy effectively improves the minimum action method to compute the spiral optimal escape path from limit cycles in various systems.
KeywordRare event Non-gradient system Quasi-potential Limit cycle Minimum action method
DOI10.1007/s00332-018-9509-3
Language英语
Funding Project100 Top Talents Program of Sun Yat-sen University[34000-18831102] ; National Natural Science Foundation of China[11871486] ; NNSFC[11771439] ; NNSFC[91530322] ; Science Challenge Project[TZ2018001] ; Research Grants Council of the Hong Kong Special Administrative Region, China[CityU 11304715] ; Research Grants Council of the Hong Kong Special Administrative Region, China[11337216] ; Research Grants Council of the Hong Kong Special Administrative Region, China[1130518]
WOS Research AreaMathematics ; Mechanics ; Physics
WOS SubjectMathematics, Applied ; Mechanics ; Physics, Mathematical
WOS IDWOS:000467546000004
PublisherSPRINGER
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/34640
Collection中国科学院数学与系统科学研究院
Corresponding AuthorZhou, Xiang
Affiliation1.Sun Yat Sen Univ, Sch Math, Guangzhou 510275, Guangdong, Peoples R China
2.Univ Chinese Acad Sci, Sch Math Sci, Beijing, Peoples R China
3.Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, NCMIS, Beijing 100190, Peoples R China
4.Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, LSEC, Beijing 100190, Peoples R China
5.City Univ Hong Kong, Sch Data Sci, Kowloon, Tat Chee Ave, Hong Kong, Peoples R China
6.City Univ Hong Kong, Dept Math, Kowloon, Tat Chee Ave, Hong Kong, Peoples R China
Recommended Citation
GB/T 7714
Lin, Ling,Yu, Haijun,Zhou, Xiang. Quasi-Potential Calculation and Minimum Action Method for Limit Cycle[J]. JOURNAL OF NONLINEAR SCIENCE,2019,29(3):961-991.
APA Lin, Ling,Yu, Haijun,&Zhou, Xiang.(2019).Quasi-Potential Calculation and Minimum Action Method for Limit Cycle.JOURNAL OF NONLINEAR SCIENCE,29(3),961-991.
MLA Lin, Ling,et al."Quasi-Potential Calculation and Minimum Action Method for Limit Cycle".JOURNAL OF NONLINEAR SCIENCE 29.3(2019):961-991.
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