Bifurcation set and distribution of limit cycles for a class of cubic Hamiltonian system with higher-order perturbed terms

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	Bifurcation set and distribution of limit cycles for a class of cubic Hamiltonian system with higher-order perturbed terms
	Cao, HJ ; Liu, ZR ; Jing, ZJ
	2000-11-01
发表期刊	CHAOS SOLITONS & FRACTALS
ISSN	0960-0779
卷号	11 期号:14 页码:2293-2304
摘要	A class of cubic Hamiltonion system with the higher-order perturbed term of degree n = 5, 7, 9, 11, 13 is investigated. We find that there exist at least 13 limit cycles with the distribution C-9(1) superset of 2[C-3(2) superset of 2C(2)(2)] (let C-m(k) denote a nest of limit cycles which encloses nl singular points, and the symbol 'subset of' is used to show the enclosing relations between limit cycles, while the sign '+' is used to divide limit cycles enclosing different critical points. Denote simply C-m(k) + C-m(k) = 2C(m)(k), etc.) in the Hamiltonian system under the perturbed term of degree 7, and give the complete bifurcation diagrams and classification of the phase portraits by using bifurcation theory and qualitative method and numerical simulations. These results in this paper are useful for the study of the weaken Hilbert 16th problem. (C) 2000 Published by Elsevier Science Ltd.
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:000088489100012
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/14979
专题	中国科学院数学与系统科学研究院
通讯作者	Cao, HJ
作者单位	1.Chinese Acad Sci, Inst Math, Beijing 100080, Peoples R China 2.Yunnan Univ, Dept Math, Inst Appl Math, Kunming 650091, Peoples R China
推荐引用方式 GB/T 7714	Cao, HJ,Liu, ZR,Jing, ZJ. Bifurcation set and distribution of limit cycles for a class of cubic Hamiltonian system with higher-order perturbed terms[J]. CHAOS SOLITONS & FRACTALS,2000,11(14):2293-2304.
APA	Cao, HJ,Liu, ZR,&Jing, ZJ.(2000).Bifurcation set and distribution of limit cycles for a class of cubic Hamiltonian system with higher-order perturbed terms.CHAOS SOLITONS & FRACTALS,11(14),2293-2304.
MLA	Cao, HJ,et al."Bifurcation set and distribution of limit cycles for a class of cubic Hamiltonian system with higher-order perturbed terms".CHAOS SOLITONS & FRACTALS 11.14(2000):2293-2304.