Hopf Cyclicity of a Family of Generic Reversible Quadratic Systems with One Center

被引：0

作者：

Ji Hua WANG ^{[1
]}

机构：

[1] School of Mathematics, Sun Yat-sen University

来源：

Acta Mathematica Sinica,English Series | 2019年 / 10期

关键词：

Quadratic reversible system; limit cycle; weak focus; Hopf bifurcation;

D O I：

暂无

中图分类号：

O175 [微分方程、积分方程];

学科分类号：

070104 ;

摘要：

This paper is concerned with small quadratic perturbations to one parameter family of generic reversible quadratic vector fields with a simple center. The first objective is to show that this system exhibits two small amplitude limit cycles emerging from a Hopf bifurcation. The second one we prove that the system has no limit cycle around the weak focus of order two. The results may be viewed as a contribution to proving the conjecture on cyclicity proposed by Iliev(1998).

引用

页码：1586 / 1594

页数：9

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