Bifurcation of Limit Cycles from a Quintic Center via the Second Order Averaging Method

被引：5

作者：

Peng, Linping ^{[1
]}

Feng, Zhaosheng F ^{[2
]}

机构：

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

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

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2015年 / 25卷 / 03期

基金：

美国国家科学基金会;

关键词：

The averaging method; bifurcation; limit cycle; period annulus; homogeneous perturbation; quintic system; QUADRATIC PERTURBATIONS; SYSTEM; SHAPE;

D O I：

10.1142/S0218127415500479

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper is concerned with the bifurcation of limit cycles from a quintic system with one center. By using the averaging theory, we show that under any small quintic homogeneous perturbations, up to order 1 in e, at most three limit cycles bifurcate from periodic orbits of the considered system, and this upper bound can be reached. Up to order 2 in e, at most seven limit cycles emerge from periodic orbits of the unperturbed one.

引用

页数：18

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