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Quasi-Periodic Solutions for Differential Equations with an Elliptic-Type Degenerate Equilibrium Point Under Small Perturbations
Li, Xuemei1; Shang, Zaijiu2,3
2019-06-01
Source PublicationJOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS
ISSN1040-7294
Volume31Issue:2Pages:653-681
AbstractThis 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.
KeywordDelay differential equation Degenerate equilibrium point Quasi-periodic solution Perturbation
DOI10.1007/s10884-018-9642-6
Language英语
Funding ProjectNNSF of China[11371132] ; NNSF of China[11671392] ; Key Laboratory of High Performance Computing and Stochastic Information Processing
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000468343600003
PublisherSPRINGER
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/34764
Collection数学所
Corresponding AuthorLi, Xuemei
Affiliation1.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
Recommended Citation
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.
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