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

作　　者：Ji Hua WANG 

机构地区：[1]School of Mathematics, Sun Yat-sen University

出　　处：《Acta Mathematica Sinica,English Series》2019年第10期1586-1594,共9页数学学报（英文版）

基　　金：Supported by the National Natural Science Foundations of China(Grant No.11601385)

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).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).

关 键 词：QUADRATIC REVERSIBLE system limit cycle WEAK focus HOPF BIFURCATION 

分 类 号：O1[理学—数学]