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

Previous Articles     Next Articles

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;;;
  • 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)


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