LIMIT CYCLES FROM A CUBIC REVERSIBLE SYSTEM VIA THE THIRD-ORDER AVERAGING METHOD

被引：0

作者：

Peng, Linping ^{[1
]}

Feng, Zhaosheng ^{[2
]}

机构：

[1] Beihang Univ, Minist Educ, Sch Math & Syst Sci, LIMB, Beijing 100191, Peoples R China

[2] Univ Texas Pan Amer, Dept Math, Edinburg, TX 78539 USA

来源：

ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS | 2015年

基金：

美国国家科学基金会;

关键词：

Bifurcation; limit cycles; homogeneous perturbation; averaging method; cubic center; period annulus; HAMILTONIAN CENTERS; QUADRATIC CENTERS; PERTURBATIONS; BIFURCATION; SHAPE;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This article concerns the bifurcation of limit cycles from a cubic integrable and non-Hamiltonian system. By using the averaging theory of the first and second orders, we show that under any small cubic homogeneous perturbation, at most two limit cycles bifurcate from the period annulus of the unperturbed system, and this upper bound is sharp. By using the averaging theory of the third order, we show that two is also the maximal number of limit cycles emerging from the period annulus of the unperturbed system.

引用

页数：27

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