Quasi-Potential Calculation and Minimum Action Method for Limit Cycle

doi:10.1007/s00332-018-9509-3

	Quasi-Potential Calculation and Minimum Action Method for Limit Cycle
	Lin, Ling 6; Yu, Haijun 3,4,5; Zhou, Xiang 1,2
刊名	JOURNAL OF NONLINEAR SCIENCE
	2019-06-01
卷号	29 期号:3 页码:961-991
关键词	Rare event Non-gradient system Quasi-potential Limit cycle Minimum action method
ISSN号	0938-8974
DOI	10.1007/s00332-018-9509-3
英文摘要	We 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.
资助项目	100 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研究方向	Mathematics ; Mechanics ; Physics
语种	英语
出版者	SPRINGER
WOS记录号	WOS:000467546000004
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/34639]
专题	中国科学院数学与系统科学研究院
通讯作者	Zhou, Xiang
作者单位	1.City Univ Hong Kong, Dept Math, Kowloon, Tat Chee Ave, Hong Kong, Peoples R China 2.City Univ Hong Kong, Sch Data Sci, Kowloon, Tat Chee Ave, Hong Kong, Peoples R China 3.Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, LSEC, Beijing 100190, Peoples R China 4.Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, NCMIS, Beijing 100190, Peoples R China 5.Univ Chinese Acad Sci, Sch Math Sci, Beijing, Peoples R China 6.Sun Yat Sen Univ, Sch Math, Guangzhou 510275, Guangdong, Peoples R China
推荐引用方式 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.