BI-CENTER PROBLEM AND HOPF CYCLICITY OF A CUBIC LIENARD SYSTEM

被引：4
|
作者：
Hu, Min [1 ]
Li, Tao [1 ]
Chen, Xingwu [1 ]
机构：
[1] Sichuan Univ, Dept Math, Chengdu 610064, Sichuan, Peoples R China
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2020年 / 25卷 / 01期
关键词：
Bi-center; Hopf cyclicity; Lienard system; limit cycle; LIMIT-CYCLES; BIFURCATIONS;
D O I：
10.3934/dcdsb.2019187
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we investigate the bi-center problem and the total Hopf cyclicity of two center-foci for the general cubic Lienard system which has three distinct equilibria and is equivalent to the general Lienard equation with cubic damping and restoring force. The location of these three equilibria is arbitrary, specially without any kind of symmetry. We find the necessary and sufficient condition for the existence of bi-centers and prove that there is no case of a unique center. On the Hopf cyclicity we prove that there are totally 9 possible styles of small amplitude limit cycles surrounding these two center-foci and 6 styles of them can occur, from which the total Hopf cyclicity is no more than 4 and no less than 2.
引用
收藏
页码：401 / 414
页数：14
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