Bifurcations of periodic solutions and chaos in Josephson system with parametric excitation

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• 作者：Shao-liang Yuan ; Zhu-jun Jing
• 关键词：Josephson system ; bifurcations ; chaos ; second ; order averaging method ; Melnikov method ; 34C23 ; 34C28 ; 34C29
• 刊名：Acta Mathematicae Applicatae Sinica, English Series
• 出版年：2015
• 出版时间：June 2015
• 年：2015
• 卷：31
• 期：2
• 页码：335-368
• 全文大小：3,972 KB
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• 作者单位：Shao-liang Yuan (1)
  Zhu-jun Jing (1) (2)
  
  1. College of Mathematics and Computer Sciences, Yichun University, Yichun, 330013, China
  2. The Center for Dynamical Systems, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China
  
• 刊物主题：Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics;
• 出版者：Institute of Applied Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
• ISSN：1618-3932

文摘

Josephson 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 β increases, etc.