The lower bounds of limit cycles for three classes of Liénard systems

XIONG Feng; HUANG Wentao

doi:10.13471/j.cnki.acta.snus.2018.06.021

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The lower bounds of limit cycles for three classes of Liénard systems

更新时间：2023-12-11

- The lower bounds of limit cycles for three classes of Liénard systems
- Acta Scientiarum Naturalium Universitatis SunYatseni Vol. 57, Issue 6, Pages: 154-161(2018)
- 作者机构：
  
  1. ．上海财经大学信息管理与工程学院,上海,200433
  2. 
- 作者简介：
- 基金信息：
- DOI：10.13471/j.cnki.acta.snus.2018.06.021
  CLC：
- Published：2018，
  
  Published Online：25 November 2018，
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XIONG Feng, HUANG Wentao. The lower bounds of limit cycles for three classes of Liénard systems. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 57(6):154-161(2018)
DOI：

XIONG Feng, HUANG Wentao. The lower bounds of limit cycles for three classes of Liénard systems. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 57(6):154-161(2018) DOI： 10.13471/j.cnki.acta.snus.2018.06.021.

摘要

分别研究了(

)=(9

7)、(

)=(8

7)和(

)=(7

8)三类Liénard系统在原点邻域内的极限环数目问题。首先，应用计算机代数软件Mathematica 和奇点量方法计算其伴随复系统的前10个，9个和9个奇点量，最后，通过雅克比行列式方法证明了这三类Liénard系统在原点充分小邻域内能够产生10个，9个和9个极限环。首次给出了H^(9

H^(8

H^(7

8)的一个下界估计，即H^(9

7)≥10

H^(8

7)≥9

H^(7

8)≥9。

Abstract

The problem of the number of limit cycles for three classes of Liénard systems

that is

(

)=(9

(

)=(8

7) and (

)=(7

are studied in the neighbourhood of the origin. The first ten

nine and nine singular point values for the corresponding accompany complex systems are calculated by using the computer algebra system

Mathematica

and the method of singular point values. Then

three kinds of Liénard system can generate at least ten

nine and nine limit cycles at the sufficiently small neighborhood of the origin respectively. And the exitence of limit cycle is proved by applying the Jacobian determinant method. It is the first time for giving the lower bound estimates for such systems

that is

H^(9

7)≥10

H^(8

7)≥9

H^(7

8)≥9.

关键词

Li&eacutenard系统奇点量细焦点极限环

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Related Author

XIONG Feng

HUANG Wentao

Wang Gaoxiong

徐兆

陈树辉

刘济科

朱洁华

Related Institution

School of Mathematics and Computational Science, Guilin University of Electronic Technology

中山大学数学系

中山大学力学系

中山大学应用力学与工程系

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