THE CENTER-FOCUS PROBLEM AND BIFURCATION OF LIMIT CYCLES IN A CLASS OF 7TH-DEGREE POLYNOMIAL SYSTEMS

被引：3
作者：
Sang, Bo [1 ,2 ]
Wang, Qinlong [2 ,3 ]
机构：
[1] Liaocheng Univ, Sch Math Sci, Liaocheng 252059, Peoples R China
[2] Hezhou Univ, Guangxi Educ Dept, Key Lab Symbol Computat & Engn Data Proc, Hezhou 542899, Guangxi, Peoples R China
[3] Hezhou Univ, Sch Sci, Hezhou 542899, Peoples R China
来源：
JOURNAL OF APPLIED ANALYSIS AND COMPUTATION | 2016年 / 6卷 / 03期
基金：
中国国家自然科学基金;
关键词：
Limit cycle; center variety; singular point value; time-reversibility; INTEGRABILITY; POINTS;
D O I：
10.11948/2016052
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
By computing singular point values, the center conditions are established for a class of 7th-degree planar polynomial systems with 15 parameters. It is proved that such systems can have 13 small-amplitude limit cycles in the neighborhood of the origin. To the best of our knowledge, this is the first example of a 7th-degree system having non-homogeneous nonlinearities with thirteen limit cycles bifurcated from a fine focus.
引用
收藏
页码：817 / 826
页数：10
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