Bifurcations and chaos in three-well Duffing system with one external forcing
文献类型：期刊论文
| 作者 | Huang, Jicai2; Jing, Zhujun1,3 |
| 刊名 | CHAOS SOLITONS & FRACTALS
 |
| 出版日期 | 2009-05-15 |
| 卷号 | 40期号:3页码:1449-1466 |
| ISSN号 | 0960-0779 |
| DOI | 10.1016/j.chaos.2007.09.045 |
| 英文摘要 | 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. |
| 资助项目 | National Natural Science Foundation of China[10671063] |
| WOS研究方向 | Mathematics ; Physics |
| 语种 | 英语 |
| WOS记录号 | WOS:000266418000047 |
| 出版者 | PERGAMON-ELSEVIER SCIENCE LTD |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/8333]  |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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