Limit cycle bifurcations by perturbing a quadratic integrable system with a triangle

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:260

Article

Xiong, Yanqin¹  Han, Maoan¹  Xiao, Dongmei² 

[1] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China

[2] Shanghai Jiao Tong Univ, Dept Math, Shanghai 200240, Peoples R China

关键词: Quadratic polynomial system;    Homoclinic loop;    Heteroclinic loop;    Triangle;    Limit cycle;   

DOI  :  10.1016/j.jde.2015.11.017

来源: Elsevier

【 摘 要 】

Finding cyclicity of homoclinic or heteroclinic loops in quadratic systems is an open problem, which is related to the second part of Hilbert's 16th problem. This paper mainly considers the problem of limit cycle bifurcation for quadratic polynomial systems near a triangle. It is proved that the cyclicity of the triangle in quadratic systems is at least three. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free