Acta mathematica scientia,Series A ›› 2020, Vol. 40 ›› Issue (3): 619-630.

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

Yi Shao(),Chunxiang A*()   

  1. 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)

Abstract:

In this paper, we study Poincaré bifurcation and Hopf bifurcation of a class of Liénard system of the form =y, =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

CLC Number: 

  • O193
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