On a cubic system with eight limit cycles

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	On a cubic system with eight limit cycles
	Ning, Shucheng 3; Xia, Bican 1,2; Zheng, Zhiming 4
	2007-10-01
发表期刊	BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN
ISSN	1370-1444
卷号	14 期号:4 页码:595-605
摘要	For a famous cubic system given by James and Lloyd, there exist some sufficient conditions such that the system has eight limit cycles. In this paper, we try to derive by computers the necessary and sufficient conditions for this system to have eight limit cycles. In order to find the symbolic real solutions to semi-algebraic systems where polynomials are Lyapunov quantities, we transform the equations into triangular systems by pseudo-division, locate the real solutions of the last equation and verify the inequalities by the Budan-Fourier theorem. The necessary and sufficient conditions for the system to have eight limit cycles are given under a reasonable limitation.
关键词	polynomial differential system limit cycle symbolic computation real solution
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000252974100001
出版者	BELGIAN MATHEMATICAL SOC TRIOMPHE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/4740
专题	中国科学院数学与系统科学研究院
通讯作者	Xia, Bican
作者单位	1.Peking Univ, LMAM, Beijing 100871, Peoples R China 2.Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China 3.Acad Sinica, Inst Math, Beijing 100080, Peoples R China 4.Beihang Univ, Beijing 100083, Peoples R China
推荐引用方式 GB/T 7714	Ning, Shucheng,Xia, Bican,Zheng, Zhiming. On a cubic system with eight limit cycles[J]. BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN,2007,14(4):595-605.
APA	Ning, Shucheng,Xia, Bican,&Zheng, Zhiming.(2007).On a cubic system with eight limit cycles.BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN,14(4),595-605.
MLA	Ning, Shucheng,et al."On a cubic system with eight limit cycles".BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN 14.4(2007):595-605.