Limit cycles near a homoclinic loop by perturbing a class of integrable systems

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:429

Article

Xiong, Yanqin¹  Han, Maoan¹ 

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

关键词: Integrable system;    Homoclinic loop;    Melnikov function;    Limit cycle;   

DOI  :  10.1016/j.jmaa.2015.04.042

来源: Elsevier

【 摘 要 】

In this paper, the problem of limit cycle bifurcation is investigated by perturbing a class of integrable systems with a homoclinic loop. Under the assumption that the homoclinic loop passes through a degenerate singular point at the origin, the asymptotic expansion of the Melnikov function along the level curves of the first integral inside the homoclinic loop is studied near the loop. Meanwhile, the formulas for the first coefficients in the expansion are given, which can be used to study the number of limit cycles near the homoclinic loop. Finally, an example is provided to demonstrate the obtained results. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free