Complex dynamics in three-well duffing system with two external forcings

doi:10.1016/j.chaos.2006.03.071

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	Complex dynamics in three-well duffing system with two external forcings
	Jing, Zhujun ; Huang, Jicai ; Deng, Jin
	2007-08-01
发表期刊	CHAOS SOLITONS & FRACTALS
ISSN	0960-0779
卷号	33 期号:3 页码:795-812
摘要	Three-well duffing system with two external forcing terms is investigated. The criterion of existence of chaos under the periodic perturbation is given by using Melnikov's method. By using second-order averaging method and Melnikov's method we proved the criterion of existence of chaos in averaged systems under quasi-periodic perturbation for omega(2) = n omega(1) + epsilon v, n = 1, 3, 5, and cannot prove the criterion of existence of chaos in second-order averaged system under quasi-periodic perturbation for omega(2) = n omega(1) + epsilon v, n = 2, 4, 6, 7, 8, 9, 10, 11, 12, where v is not rational to omega(1), but can show the occurrence of chaos in original system by numerical simulation. Numerical simulations including heteroclinic and homoclinic bifurcation surfaces, bifurcation diagrams, maximum Lyapunov exponents and Poincare map are given to illustrate the theoretical analysis, and to expose the more new complex dynamical behaviors. We show that cascades of period-doubling bifurcations from period-one to four orbits, cascades of interlocking period-doubling bifurcations from period-two orbits of two sets, from quasi-periodicity leading to chaos, onset of chaos which occurs more than one, interleaving occurrences of chaotic behavior and invariant torus, transient chaos with complex period windows and interior crisis, chaos converting to torus, different kind of chaotic attractors. Our results shows that the dynamical behaviors are different from the dynamics of duffing equation with two-well and two external forcings. (c) 2006 Elsevier Ltd. All rights reserved.
DOI	10.1016/j.chaos.2006.03.071
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:000246259400009
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/4659
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, Beijing 100080, Peoples R China 2.Hunan Normal Univ, Dept Math, Hunan Changsha 410081, Peoples R China 3.Cent China Normal Univ, Sch Math & Stat, Hubei Wuhan 430079, Peoples R China 4.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Jing, Zhujun,Huang, Jicai,Deng, Jin. Complex dynamics in three-well duffing system with two external forcings[J]. CHAOS SOLITONS & FRACTALS,2007,33(3):795-812.
APA	Jing, Zhujun,Huang, Jicai,&Deng, Jin.(2007).Complex dynamics in three-well duffing system with two external forcings.CHAOS SOLITONS & FRACTALS,33(3),795-812.
MLA	Jing, Zhujun,et al."Complex dynamics in three-well duffing system with two external forcings".CHAOS SOLITONS & FRACTALS 33.3(2007):795-812.