Bifurcations and chaos in three-well Duffing system with one external forcing

doi:10.1016/j.chaos.2007.09.045

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	Bifurcations and chaos in three-well Duffing system with one external forcing
	Huang, Jicai 2; Jing, Zhujun 1,3
	2009-05-15
发表期刊	CHAOS SOLITONS & FRACTALS
ISSN	0960-0779
卷号	40 期号:3 页码:1449-1466
摘要	The dynamics of three-well Duffing system with one external forcing are investigated in detail. The conditions of existence and bifurcations for harmonics, subharmonics (second-order, third-order and m-order) and superharmonics under small perturbations are given by using second-order averaging method and Melnikov's method, the threshold values of chaotic motion under periodic perturbation are also given by Melnikov's method. Moreover, the numerical simulations (including bifurcation curves, bifurcation diagrams in three-dimensional space and two-dimensional plane, phase portraits,. leading Lyapunov Exponents and homoclinic and heteroclinic bifurcation surfaces in three-dimensional parametric space) not only show the consistence with the theoretical analyses but also exhibit more new complex dynamical behaviors, including cascades of period-doubling and reverse period doubling bifurcations, complex period windows, onset of chaos, symmetry-breaking, intermittent dynamics, different chaotic attractors, quasi-periodic orbits, and the system can leave the chaotic behavior to period-one orbit as Parameters a, delta(1) and gamma(1) increase. Combining the existing results of Li and Moon in 1990 with the new results reported in this paper, a more complete description of the system is now obtained. (C) 2007 Elsevier Ltd. All rights reserved.
DOI	10.1016/j.chaos.2007.09.045
语种	英语
资助项目	National Natural Science Foundation of China[10671063]
WOS研究方向	Mathematics ; Physics
WOS类目	Mathematics, Interdisciplinary Applications ; Physics, Multidisciplinary ; Physics, Mathematical
WOS记录号	WOS:000266418000047
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/8334
专题	中国科学院数学与系统科学研究院
通讯作者	Jing, Zhujun
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Ctr Dynam Syst, Beijing 100080, Peoples R China 2.Cent China Normal Univ, Sch Math & Stat, Hubei Wuhan 430079, Peoples R China 3.Hunan Normal Univ, Dept Math, Hunan Changsha 410081, Peoples R China
推荐引用方式 GB/T 7714	Huang, Jicai,Jing, Zhujun. Bifurcations and chaos in three-well Duffing system with one external forcing[J]. CHAOS SOLITONS & FRACTALS,2009,40(3):1449-1466.
APA	Huang, Jicai,&Jing, Zhujun.(2009).Bifurcations and chaos in three-well Duffing system with one external forcing.CHAOS SOLITONS & FRACTALS,40(3),1449-1466.
MLA	Huang, Jicai,et al."Bifurcations and chaos in three-well Duffing system with one external forcing".CHAOS SOLITONS & FRACTALS 40.3(2009):1449-1466.