Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (4): 936-953.

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Bifurcation of Limit Cycles from a Liénard System of Degree 4

Hongying Zhu1(),Minzhi Wei1(),Sumin Yang2,*(),Caoqing Jiang1()   

  1. 1 Department of Applied Mathematics, Guangxi University of Finance and Economics, Nanning 530003
    2 Department of Public Teaching, Guangxi Technological College of Machinery and Electricity, Nanning 530003
  • Received:2020-05-14 Online:2021-08-26 Published:2021-08-09
  • Contact: Sumin Yang E-mail:zhy71118@163.com;454742516@qq.com;smyang125@126.com;86072787@qq.com
  • Supported by:
    the NSFC(11861009);the NSFC(11761011);the NSF of Guangxi(2020JJB110007);the Middle-Aged and Young Teachers' Basic Ability Promotion Project in Guangxi and Scientific Research Project(2020KY16020)

Abstract:

In this paper, we study the number of limit cycles by Poincaré bifurcation for some Liénard system of degree 4. We prove that the system can bifurcate at most 6 limit cycles from the periodic annulus, by the tools of regular chain theory in polynomial algebra and Chebyshev criteria, at least 3 limit cycles by asymptotic expansions of the related Abelian integral (first order Melnikov functions).

Key words: Liénard system, Chebyshev system, Melnikov functions, Weak Hilbert's 16th problem

CLC Number: 

  • O175.12
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