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Complex dynamics in Duffing-Van der Pol equation
Jing, ZJ; Yang, ZY; Jiang, T
2006-02-01
Source PublicationCHAOS SOLITONS & FRACTALS
ISSN0960-0779
Volume27Issue:3Pages:722-747
AbstractDuffing-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.
DOI10.1016/j.chaos.2005.04.044
Language英语
WOS Research AreaMathematics ; Physics
WOS SubjectMathematics, Interdisciplinary Applications ; Physics, Multidisciplinary ; Physics, Mathematical
WOS IDWOS:000232193700016
PublisherPERGAMON-ELSEVIER SCIENCE LTD
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/2792
Collection中国科学院数学与系统科学研究院
Corresponding AuthorJing, ZJ
Affiliation1.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
Recommended Citation
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.
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