利用任意阶Melnikov函数方法研究一类二次近可积系统的极限环分支  

Using the Melnikov Function Method of Any Order to Study the Bifurcation of Limit Cycles for A Class of Quadratic Near Integrable Systems

作　　者：施吕蓉[1,2] SHI Lv-rong(Department of Foundational Teaching,Wuhu Institute of Technology;School of Mathematics and Statistics,Anhui Normal Unirersity,Wuhu 241000,China)

机构地区：[1]芜湖职业技术学院基础教学部 [2]安徽师范大学数学与统计学院,芜湖241000

出　　处：《西安文理学院学报（自然科学版）》2020年第3期7-11,共5页Journal of Xi’an University(Natural Science Edition)

基　　金：2016年度安徽省教育厅自然科学研究项目(KJ2016A760);2017年度校级“教学质量与教学改革工程”项目;2020年度校级自然科学重点项目(Wzyzrzd202006).

摘　　要：应用任意阶Melnikov函数方法,研究了一类具奇直线的二次系统的扰动分支.证明了当扰动项亦为二次时,系统至多可分支出2个极限环,且可出现2个环.从而校正了已有文献的相关结果.In this paper,the perturbation bifurcation of a class of quadratic system with singular line is studied by using the Melnikov function method of any order.It is proved that when the disturbance term is quadratic,the system can branch out two limit cycles at most,and two cycles can appear.Thus,the related results of the existing literature are corrected.

关 键 词：近可积系统 极限环 MELNIKOV函数 

分 类 号：O175[理学—数学]