The bifurcation of limit cycles of two classes of cubic isochronous systems

被引：0

作者：

Shao, Yi ^{[1
]}

Lai, Yongzeng ^{[2
]}

A, Chunxiang ^{[1
]}

机构：

[1] Zhaoqing Univ, Sch Math & Stat, Zhaoqing 526061, Guangdong, Peoples R China

[2] Wilfrid Laurier Univ, Dept Math, Waterloo, ON N2L 3C5, Canada

来源：

ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS | 2019年 / 50期

关键词：

limit cycle; period annulus; cubic perturbations; PERIOD ANNULUS; PERTURBATIONS; CYCLICITY; DEGREE-4; INTEGRALS; SADDLE; LOOP;

D O I：

10.14232/ejqtde.2019.1.50

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the bifurcation of limit cycles of the periodic annulus of two classes of cubic isochronous systems. By using complete elliptic integrals of the first, second kinds and the Chebyshev criterion, we show that the upper bound for the number of limit cycles which appear from the periodic annuli of the two systems are at least three under cubic perturbations. Moreover, there exists a perturbation that give rise to exactly i limit cycles bifurcating from the period annulus for each i = 0,1, 2, 3.

引用

页数：15

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