Limit cycle bifurcations by perturbing a class of integrable systems with a polycycle

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:418

Article

Wang, Yanqin^1,2  Han, Maoan¹ 

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

[2] Changzhou Univ, Sch Math & Phys, Changzhou 213164, Jiangsu, Peoples R China

关键词: Heteroclinic loop;    Near-integrable system;    Melnikov function;    Limit cycle bifurcation;   

DOI  :  10.1016/j.jmaa.2014.03.091

来源: Elsevier

【 摘 要 】

In this paper, we deal with the problem of limit cycle bifurcation near a 2-polycycle or 3-polycycle for a class of integrable systems by using the first order Melnikov function. We first get the formal expansion of the Melnikov function corresponding to the heteroclinic loop and then give some computational formulas for the first coefficients of the expansion. Based on the coefficients, we obtain a lower bound for the maximal number of limit cycles near the polycycle. As an application of our main results, we consider quadratic integrable polynomial systems, obtaining at least two limit cycles. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free