Complex dynamics in pendulum equation with parametric and external excitations I

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	Complex dynamics in pendulum equation with parametric and external excitations I
	Jing, Zhujun ; Yang, Jianping
	2006-10-01
发表期刊	INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
ISSN	0218-1274
卷号	16 期号:10 页码:2887-2902
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.
关键词	pendulum equation Melnikov's method bifurcations chaos
语种	英语
WOS研究方向	Mathematics ; Science & Technology - Other Topics
WOS类目	Mathematics, Interdisciplinary Applications ; Multidisciplinary Sciences
WOS记录号	WOS:000243320500007
出版者	WORLD SCIENTIFIC PUBL CO PTE 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/3921
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.