Quasi-Periodic Solutions for Differential Equations with an Elliptic-Type Degenerate Equilibrium Point Under Small Perturbations

doi:10.1007/s10884-018-9642-6

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	Quasi-Periodic Solutions for Differential Equations with an Elliptic-Type Degenerate Equilibrium Point Under Small Perturbations
	Li, Xuemei 1; Shang, Zaijiu2,3
	2019-06-01
发表期刊	JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS
ISSN	1040-7294
卷号	31 期号:2 页码:653-681
摘要	This work focuses on the existence of quasi-periodic solutions for ordinary and delay differential equations (ODEs and DDEs for short) with an elliptic-type degenerate equilibrium point under quasi-periodic perturbations. We prove that under appropriate hypotheses there exist quasi-periodic solutions for perturbed ODEs and DDEs near the equilibrium point for most parameter values, then apply these results to the delayed van der Pol's oscillator with zero-Hopf singularity.
关键词	Delay differential equation Degenerate equilibrium point Quasi-periodic solution Perturbation
DOI	10.1007/s10884-018-9642-6
语种	英语
资助项目	NNSF of China[11371132] ; NNSF of China[11671392] ; Key Laboratory of High Performance Computing and Stochastic Information Processing
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000468343600003
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/34764
专题	数学所
通讯作者	Li, Xuemei
作者单位	1.Hunan Normal Univ, Dept Math, Key Lab High Performance Comp & Stochast Informat, Changsha 410081, Hunan, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, HLM, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Li, Xuemei,Shang, Zaijiu. Quasi-Periodic Solutions for Differential Equations with an Elliptic-Type Degenerate Equilibrium Point Under Small Perturbations[J]. JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS,2019,31(2):653-681.
APA	Li, Xuemei,&Shang, Zaijiu.(2019).Quasi-Periodic Solutions for Differential Equations with an Elliptic-Type Degenerate Equilibrium Point Under Small Perturbations.JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS,31(2),653-681.
MLA	Li, Xuemei,et al."Quasi-Periodic Solutions for Differential Equations with an Elliptic-Type Degenerate Equilibrium Point Under Small Perturbations".JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS 31.2(2019):653-681.