Global dynamics of a Wilson polynomial Lienard equation

Release time:2020-02-21

Journal:Proccedings of the American Mathematical Society

Abstract:Gasull and Sabatini in [Ann. Mat. Pura Appl., 2019] studied limit cycles of a Li enard system which has a xed invariant curve, i.e., a Wilson polynomial Li enard system. The Li enard system can be changed into $\dot x=y-(x^2-1)(x^3-bx), ~ \dot y=-x(1+y(x^3-bx))$. For $b\leq0.7 limit cycles of the system are studied completely. But, for 0.7 < b < 0.76, the exact number of limit cycles is still unknown, and Gasull and Sabatini conjectured that the exact number of limit cycles is two(including multiplicities). In this paper, we give a positive answer of this conjecture and study all bifurcatio

First Author:Chen Haibo

Indexed by:Journal paper

Correspondence Author:Chen Hebai*

Discipline:数学

Document Type:J

Volume:148

Issue:11

Page Number:4769-4780

Translation or Not:no

Included Journals:SCI