Complex dynamics in Josephson system with two external forcing terms

doi:10.1016/j.chaos.2005.08.156

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	Complex dynamics in Josephson system with two external forcing terms
	Yang, JP ; Feng, W ; Jing, ZJ
	2006-10-01
发表期刊	CHAOS SOLITONS & FRACTALS
ISSN	0960-0779
卷号	30 期号:1 页码:235-256
摘要	Josephson system with two external forcing terms is investigated. By applying Melnikov method, we prove that criterion of existence of chaos under periodic perturbation. By second-order averaging method and Melnikov method, we obtain the criterion of existence of chaos in averaged system under quasi-periodic perturbation for omega(2)=omega(1) + epsilon nu, and cannot prove the criterion of existence of chaos in averaged system under quasi-periodic perturbation for omega(2)=n omega(1) + epsilon nu (n >= 2 and n epsilon N), where nu is not rational to omega(1). We also study the effects of the parameters of system on dynamical behaviors by using numerical simulation. The numerical simulations, including bifurcation diagram of fixed points, bifurcation diagram of system in three- and two-dimensional space, homoclinic and heteroclinic bifurcation surface, Maximum Lyapunov exponent, phase portraits, Poincare map, are also plotted to illustrate theoretical analysis, and to expose the complex dynamical behaviors, including the period-n (n = 1, 2, 5,7) orbits in different chaotic regions, cascades of period-doubling bifurcation from period-1, 2 and 5 orbits, reverse period-doubling bifurcation, onset of chaos which occurs more than once for two given external frequencies and chaos suddenly converting to periodic orbits, transient chaos with complex periodic windows and crisis, reverse period-5 bubble, non-attracting chaotic set and nice attracting chaotic set. In particular, we observe that the system can leave chaotic region to periodic motion by adjusting damping alpha, amplitude f(1) and frequency omega(2) of external forcing which can be considered as a control strategy. (c) 2005 Elsevier Ltd. All rights reserved.
DOI	10.1016/j.chaos.2005.08.156
语种	英语
WOS研究方向	Mathematics ; Physics
WOS类目	Mathematics, Interdisciplinary Applications ; Physics, Multidisciplinary ; Physics, Mathematical
WOS记录号	WOS:000238271700026
出版者	PERGAMON-ELSEVIER SCIENCE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/2621
专题	中国科学院数学与系统科学研究院
通讯作者	Jing, ZJ
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China 2.Beihang Univ, Dept Math, Beijing 100083, Peoples R China 3.Hunan Normal Univ, Dept Math, Changsha 410081, Peoples R China 4.Chinese Acad Sci, Grad Sch, Beijing 100039, Peoples R China
推荐引用方式 GB/T 7714	Yang, JP,Feng, W,Jing, ZJ. Complex dynamics in Josephson system with two external forcing terms[J]. CHAOS SOLITONS & FRACTALS,2006,30(1):235-256.
APA	Yang, JP,Feng, W,&Jing, ZJ.(2006).Complex dynamics in Josephson system with two external forcing terms.CHAOS SOLITONS & FRACTALS,30(1),235-256.
MLA	Yang, JP,et al."Complex dynamics in Josephson system with two external forcing terms".CHAOS SOLITONS & FRACTALS 30.1(2006):235-256.