Complex dynamics in pendulum equation with parametric and external excitations II
文献类型：期刊论文
| 作者 | Jing, Zhujun; Yang, Jianping |
| 刊名 | INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
 |
| 出版日期 | 2006-10-01 |
| 卷号 | 16期号:10页码:3053-3078 |
| 关键词 | pendulum equation averaging method Melnikov's method bifurcations quasiperiodicity chaos |
| ISSN号 | 0218-1274 |
| 英文摘要 | This paper (II) is a continuation of "Complex dynamics in pendulum equation with parametric and external excitations (I)." By applying second-order averaging method and Melnikov's method, we obtain the criterion of existence of chaos in an averaged system under quasi-periodic perturbation for Omega = n omega + epsilon v, n = 1, 2,4 and cannot prove the criterion of existence of chaos in averaged system under quasi-periodic perturbation for Omega = n omega + epsilon v, n = 3, 5-15 by Melnikov's method, where v is not rational to omega. However, we show the occurrence of chaos in the averaged and original systems under quasi-periodic perturbation for Omega = n omega + epsilon V, n 3, 5 by numerical simulation. The numerical simulations, include the bifurcation diagram of fixed points, bifurcation diagrams in three- and two-dimensional spaces, homoclinic bifurcation surface, maximum Lyapunov exponent, phase portraits, Poincare map, are plotted to illustrate theoretical analysis, and to expose the complex dynamical behaviors, including period-3 orbits in different chaotic regions, interleaving occurrence of chaotic behaviors and quasi-periodic behaviors, a different kind of interior crisis, jumping behavior of quasi-periodic sets, different nice quasi-periodic attractors, nonchaotic attractors and chaotic attractors, coexistence of three quasi-periodic sets, onset of chaos which occurs more than once for a given external frequency or amplitudes, and quasi-periodic route to chaos. We do not find the period-doubling cascade. The dynamical behaviors under quasi-periodic perturbation are different from that of periodic perturbation. |
| WOS研究方向 | Mathematics ; Science & Technology - Other Topics |
| 语种 | 英语 |
| WOS记录号 | WOS:000243320500020 |
| 出版者 | WORLD SCIENTIFIC PUBL CO PTE LTD |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/2913]  |
| 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, Changsha 410081, Peoples R China 3.Chinese Acad Sci, Grad Sch, Beijing 100039, Peoples R China |
| 推荐引用方式 GB/T 7714 | Jing, Zhujun,Yang, Jianping. Complex dynamics in pendulum equation with parametric and external excitations II[J]. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS,2006,16(10):3053-3078. |
| APA | Jing, Zhujun,&Yang, Jianping.(2006).Complex dynamics in pendulum equation with parametric and external excitations II.INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS,16(10),3053-3078. |
| MLA | Jing, Zhujun,et al."Complex dynamics in pendulum equation with parametric and external excitations II".INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS 16.10(2006):3053-3078. |
入库方式： OAI收割
来源：数学与系统科学研究院
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