Complex dynamics in pendulum equation with parametric and external excitations I
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:2887-2902 |
| 关键词 | pendulum equation Melnikov's method bifurcations chaos |
| ISSN号 | 0218-1274 |
| 英文摘要 | Pendulum equation with parametric and external excitations is investigated in (1) and (II). In (1), by applying Melnikov's method, we prove the criterion of existence of chaos under periodic perturbation. The numerical simulations, including bifurcation diagram of fixed points, bifurcation diagram of system in three- and two-dimensional space, homoclinic and heteroclinic bifurcation surface, Maximum Lyapunov exponent, phase portraits, Poincare map, are plotted to illustrate theoretical analysis, and to expose the complex dynamical behaviors including the period-n (n = 2 to 6, 10, 15 and 20) orbits in different chaotic regions, interlocking periodic orbits, symmetry-breaking of periodic orbit, cascade of period-doubling bifurcations from period-5 and -10 orbits, reverse period-doubling bifurcation, onset of chaos which occurs more than once for a given external frequency or parametric frequency and chaos suddenly converting to periodic orbits, sudden jump in the size of attractors which is associated with the transverse intersection of stable and unstable manifolds of perturbed saddle, hopping behavior of chaos, transient chaos with complex periodic windows and interior crisis, varied chaotic attractors including the more than three-band and eight-band chaotic attractors, chaotic attractor after strange nonchaotic attractor. In particular, we observe that the system can leave chaotic region to periodic motion by adjusting damping delta, spring constant alpha and frequency Omega of parametric excitation which can be considered as a control strategy. In (11), we will investigate the complex dynamics under quasi-periodic perturbation. |
| WOS研究方向 | Mathematics ; Science & Technology - Other Topics |
| 语种 | 英语 |
| WOS记录号 | WOS:000243320500007 |
| 出版者 | WORLD SCIENTIFIC PUBL CO PTE LTD |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/3920]  |
| 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 I[J]. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS,2006,16(10):2887-2902. |
| APA | Jing, Zhujun,&Yang, Jianping.(2006).Complex dynamics in pendulum equation with parametric and external excitations I.INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS,16(10),2887-2902. |
| MLA | Jing, Zhujun,et al."Complex dynamics in pendulum equation with parametric and external excitations I".INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS 16.10(2006):2887-2902. |
入库方式： OAI收割
来源：数学与系统科学研究院
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