Bifurcations of Periodic Solutions and Chaos in Josephson System with Parametric Excitation  

作　　者：Shao-liang YUAN Zhu-jun JING 

机构地区：[1]College of Mathematics and Computer Sciences, Yichun University [2]The Center for Dynamical Systems, Academy of Mathematics and Systems Science, Chinese Academy of Sciences

出　　处：《Acta Mathematicae Applicatae Sinica》2015年第2期335-368,共34页应用数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China(No.11361037,11371132);the Natural Science Foundation of Hunan Province(No.11JJ3012);the Graduate Innovation Fund of Hunan Province(No.CX2011B183)

摘　　要：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, symmetrybreaking, 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.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, symmetrybreaking, 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.

关 键 词：Josephson system BIFURCATIONS CHAOS second-order averaging method Melnikov method 

分 类 号：O175[理学—数学]