BIFURCATION OF LIMIT CYCLES FROM A COMPOUND LOOP WITH FIVE SADDLES

被引：6

作者：

Sheng, Lijuan ^{[1
]}

Han, Maoan ^{[1
,2
]}

机构：

[1] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China

[2] Zhejiang Normal Univ Jinhua, Dept Math, Jinhua 321004, Zhejiang, Peoples R China

来源：

JOURNAL OF APPLIED ANALYSIS AND COMPUTATION | 2019年 / 9卷 / 06期

基金：

中国国家自然科学基金;

关键词：

Limit cycle; bifurcation; Melnikov function; homoclinic loop; 16TH HILBERT PROBLEM; SYSTEMS; 2-POLYCYCLE; CYCLICITY;

D O I：

10.11948/20190342

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We concern the number of limit cycles of a polynomial system with degree nine. We prove that under different conditions, the system can have 12 and 20 limit cycles bifurcating from a compound loop with five saddles. Our method relies upon the Melnikov function method and the method of stability-changing of a double homoclinic loop proposed by the authors[J. Yang, Y. Xiong and M. Han, Nonlinear Anal-Theor., 2014, 95, 756-773].

引用

页码：2482 / 2495

页数：14

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