Complex dynamics in Duffing-Van der Pol equation

doi:10.1016/j.chaos.2005.04.044

	Complex dynamics in Duffing-Van der Pol equation
	Jing, ZJ ; Yang, ZY ; Jiang, T
刊名	CHAOS SOLITONS & FRACTALS
	2006-02-01
卷号	27 期号:3 页码:722-747
ISSN号	0960-0779
DOI	10.1016/j.chaos.2005.04.044
英文摘要	Duffing-Van der Pol equation with fifth nonlinear-restoring force and two external forcing terms is investigated. The threshold values of existence of chaotic motion are obtained under the periodic perturbation. By second-order averaging method and Melnikov method, we prove the criterion of existence of chaos in averaged system under quasi-periodic perturbation for omega(2) = n omega(1) + epsilon sigma, 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 sigma, n = 2, 4, 6, 7, 8, 9, 10, where a 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, Lyapunov exponent, phase portraits and Poincare map, not only show the consistence with the theoretical analysis but also exhibit the more new complex dynamical behaviors. We show that cascades of interlocking period-doubling and reverse period-doubling bifurcations from period-2 to -4 and -6 orbits, interleaving occurrence of chaotic behaviors and quasi-periodic orbits, transient chaos with a great abundance of period windows, symmetry-breaking of periodic orbits in chaotic regions, onset of chaos which occurs more than one, chaos suddenly disappearing to period orbits, interior crisis, strange non-chaotic attractor, non-attracting chaotic set and nice chaotic attractors. Our results show many,dynamical behaviors and some of them are strictly departure from the behaviors of Duffing-Van der Pot equation with a cubic nonlinear-restoring force and one external forcing. (c) 2005 Elsevier Ltd. All rights reserved.
WOS研究方向	Mathematics ; Physics
语种	英语
出版者	PERGAMON-ELSEVIER SCIENCE LTD
WOS记录号	WOS:000232193700016
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/2791]
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.Hunan Normal Univ, Dept Math, Changsha 410081, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China 3.Chinese Acad Sci, Grad Sch, Beijing 100039, Peoples R China
推荐引用方式 GB/T 7714	Jing, ZJ,Yang, ZY,Jiang, T. Complex dynamics in Duffing-Van der Pol equation[J]. CHAOS SOLITONS & FRACTALS,2006,27(3):722-747.
APA	Jing, ZJ,Yang, ZY,&Jiang, T.(2006).Complex dynamics in Duffing-Van der Pol equation.CHAOS SOLITONS & FRACTALS,27(3),722-747.
MLA	Jing, ZJ,et al."Complex dynamics in Duffing-Van der Pol equation".CHAOS SOLITONS & FRACTALS 27.3(2006):722-747.