一类(5,10)次Liénard方程的小振幅极限环（英文）  

Small-amplitude limit cycles for class of(m=5,n=10) Liénard system

作　　者：蔡俊宁[1,2] 黄文韬 韦敏志 Cai Junning;Huang Wentao;Wei Minzhi(School of Information and Statistics,Guangxi University of Finance and Economics,Nanning,Guangxi 530000,China;College of Science Guilin University of Aerospace Technology,Guilin,Guangxi 530004,China)

机构地区：[1]广西财经学院应用数学系,广西南宁530003 [2]桂林航空航天工业学院理学部,广西桂林541004

出　　处：《上海师范大学学报（自然科学版）》2018年第3期383-388,共6页Journal of Shanghai Normal University(Natural Sciences)

基　　金：The National Natural Science Foundation of China(11261013);Guangxi University of Finance and Economics Youth Teachers Based capacity Building(2017QN09;2016A006)

摘　　要：研究了一类m=5,n=10次Liénard系统在原点邻域的极限环数目问题,先通过计算机符号计算出原点的奇点量,再通过行列式方法证明了系统原点充分小邻域能产生9个极限环.给出了H(5,10)的一个新下界,即H(5,10)≥9.We studied the number of limit cycles for the class of Li6naxd system （m=5,n=10neighborhood of the origin is studied. We proved that nine small amplitude limit cycles could bifurcate from the origin by using computer symbolic computation to compute singular point values and using the method of Jacobi determinant. It is a new lower bound estimate on Lidnard system in the case of m is equal to five and n is equal to ten, that is H（5, 10）≥ 9.

关 键 词：LIÉNARD系统 奇点量 细焦点 极限环 

分 类 号：O193[理学—数学]