具有尖点的四次Liénard系统的极限环分支

数学物理学报 ›› 2020, Vol. 40 ›› Issue (3): 619-630.

具有尖点的四次Liénard系统的极限环分支

邵仪(),阿春香*()

^{肇庆学院数学与统计学院广东肇庆 526061}

收稿日期:2019-04-16 出版日期:2020-06-26 发布日期:2020-07-15
通讯作者: 阿春香 E-mail:mathsyishao@126.com;acxgmaria@hotmail.com
作者简介:邵仪, E-mail:mathsyishao@126.com
基金资助:
国家自然科学基金(11571379);国家自然科学基金(11661017);国家自然科学基金(71801186);广东省自然科学基金(2017A030310660);教育部人文社会科学基金(18YJC630001)

Limit Cycles Bifurcations of Liénard System of Degree Four with One Nilpotent Cusp

Yi Shao(),Chunxiang A*()

^{School of Mathematics and Statistics, Zhaoqing University, Guangdong Zhaoqing 526061}

Received:2019-04-16 Online:2020-06-26 Published:2020-07-15
Contact: Chunxiang A E-mail:mathsyishao@126.com;acxgmaria@hotmail.com
Supported by:
the NSFC(11571379);the NSFC(11661017);the NSFC(71801186);the NSF of Guangdong Province(2017A030310660);the Science Foundation of Ministry of Education(18YJC630001)

摘要/Abstract

摘要：

该文研究了一类形如ẋ=y，ẏ=f（x）+εg（x）y的Liénard系统的Poincaré分支和Hopf分支，其中f（x）和g（x）分别是4次和3次多项式，证明了该系统绕原点最多能够产生3个极限环.

关键词: Liénard系统, 极限环, 分支

Abstract:

In this paper, we study Poincaré bifurcation and Hopf bifurcation of a class of Liénard system of the form ẋ=y, ẏ=f(x)+εg(x)y, where f(x) and g(x) are polynomials of degree 4 and 3, respectively. It is proven that this system can produce at most three limit cycles surrounding the origin.

Key words: Liénard system, Limit cycles, Bifurcations

中图分类号:

O193

邵仪,阿春香. 具有尖点的四次Liénard系统的极限环分支[J]. 数学物理学报, 2020, 40(3): 619-630.

Yi Shao,Chunxiang A. Limit Cycles Bifurcations of Liénard System of Degree Four with One Nilpotent Cusp[J]. Acta mathematica scientia,Series A, 2020, 40(3): 619-630.

图/表 1

参考文献 25

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