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

页码：817 / 826

页数：10

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