A proof of Wang-Kooij's conjectures for a cubic Lienard system with a cusp

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:445

Article

Chen, Hebai¹  Chen, Xingwu² 

[1] Southwest Jiaotong Univ, Sch Mech & Engn, Chengdu 610031, Sichuan, Peoples R China

[2] Sichuan Univ, Dept Math, Chengdu 610064, Sichuan, Peoples R China

关键词: Lienard system;    Cuspidal loop;    Limit cycle;    Rotational vector field;   

DOI  :  10.1016/j.jmaa.2016.08.008

来源: Elsevier

【 摘 要 】

In this paper the global dynamics of a cubic Lienard system with a cusp is studied to follow Wang and Kooij (1992) [13], who proved that the maximum number of limit cycles is 2 and stated two conjectures about the curves of the cuspidal loop bifurcation and the double limit cycle bifurcation. We give positive answers to those two conjectures and further properties of those bifurcation curves such as monotonicity and smoothness. Finally, associated with previous results we obtain the complete bifurcation diagram and all phase portraits, and demonstrate some numerical examples. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free