关于Lienard系统极限环的研究综述

数学理论与应用 ›› 2021, Vol. 41 ›› Issue (3): 59-95.

关于Lienard系统极限环的研究综述

杨若成¹，杨柳青²，唐异垒 ¹

1. 上海交通大学数学科学学院，上海 200240; 2. 福州大学数学与计算机科学学院，福州 350108

出版日期:2021-09-30 发布日期:2021-10-28

Some Research on Limit Cycles of Li\'enard System

1. School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, 200240, China; 2. College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350108, China

Online:2021-09-30 Published:2021-10-28
Contact: Ruocheng Yang(1999−), Male, Shanghai, Undergraduate; E−mail：magic-earvin-johnson@sjtu.edu.cn
Supported by:
The first author is supported by the National Undergraduate Innovative Practice Program of SJTU [No. IPP22089]

摘要/Abstract

摘要： 本文介绍了Li\'enard系统极限环的研究进展及最近的一些结果.从四个方面来阐述这些结果：极限环的存在性、极限环的唯一性、极限环的确切数目和极限环个数的上界.最后，我们总结了研究Li\'enard系统极限环的一些方法.

关键词: 极限环, Li\'enard系统; , 极限环的存在唯一性; , 极限环的确切数目

Abstract: The aim of this paper is to introduce the progress on the research for limit cycles of Li\'enard systems and present some new results. The results focus on four problems: the existence of limit cycles, the uniqueness of limit cycles, the exact number of limit cycles and the upper bound of limit cycles. Finally, we summarize some methods for studying limit cycles of Li\'enard systems.

Key words: Limit cycle; , Li\'enard system; , Existence and uniqueness of limit cycles; , Exact number oflimit cycles

杨若成, 杨柳青, 唐异垒 . 关于Lienard系统极限环的研究综述[J]. 数学理论与应用, 2021, 41(3): 59-95.