KMS Of Academy of mathematics and systems sciences, CAS
Complex dynamics in Duffing-Van der Pol equation | |
Jing, ZJ; Yang, ZY; Jiang, T | |
2006-02-01 | |
发表期刊 | CHAOS SOLITONS & FRACTALS |
ISSN | 0960-0779 |
卷号 | 27期号:3页码:722-747 |
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. |
DOI | 10.1016/j.chaos.2005.04.044 |
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:000232193700016 |
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/2792 |
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. |
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