Bifurcations of Periodic Solutions and Chaos in Josephson System with Parametric Excitation
Yuan, Shao-liang1; Jing, Zhu-jun1,2
AbstractJosephson system with parametric excitation is investigated. Using second-order averaging method and Melnikov function, we analyze the existence and bifurcations for harmonic, (2, 3, n-order) subharmonics and (2, 3-order) superharmonics and the heterocilinic and homoclinic bifurcations for chaos under periodic perturbation. Using numerical simulation, we check our theoretical analysis and further study the effect of the parameters on dynamics. We find the complex dynamics, including the jumping behaviors, symmetry-breaking, chaos converting to periodic orbits, interior crisis, non-attracting chaotic set, interlocking (reverse) period-doubling bifurcations from periodic orbits, the processes from interlocking period-doubling bifurcations of periodic orbits to chaos after strange non-chaotic motions when the parameter beta increases, etc.
KeywordJosephson system bifurcations chaos second-order averaging method Melnikov method
Funding ProjectNational Natural Science Foundation of China[11361037] ; National Natural Science Foundation of China[11371132] ; Natural Science Foundation of Hunan Province[11JJ3012] ; Graduate Innovation Fund of Hunan Province[CX2011B183]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000355060400006
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Document Type期刊论文
Corresponding AuthorJing, Zhu-jun
Affiliation1.Yichun Univ, Coll Math & Comp Sci, Yichun 330013, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, Ctr Dynam Syst, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Yuan, Shao-liang,Jing, Zhu-jun. Bifurcations of Periodic Solutions and Chaos in Josephson System with Parametric Excitation[J]. ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES,2015,31(2):335-368.
APA Yuan, Shao-liang,&Jing, Zhu-jun.(2015).Bifurcations of Periodic Solutions and Chaos in Josephson System with Parametric Excitation.ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES,31(2),335-368.
MLA Yuan, Shao-liang,et al."Bifurcations of Periodic Solutions and Chaos in Josephson System with Parametric Excitation".ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES 31.2(2015):335-368.
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