On the independent perturbation parameters and the number of limit cycles of a type of Lienard system

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:464

Article

Yang, Junmin^1,2  Yu, Pei²  Sun, Xianbo³ 

[1] Hebei Normal Univ, Coll Math & Informat Sci, Shijiazhuang 050024, Hebei, Peoples R China

[2] Western Univ, Dept Appl Math, London, ON N6A 5B7, Canada

[3] Guangxi Univ Finance & Econ, Dept Appl Math, Nanning 530003, Guangxi, Peoples R China

关键词: Lienard system;    Independent parameter;    Limit cycle;   

DOI  :  10.1016/j.jmaa.2018.04.020

来源: Elsevier

【 摘 要 】

In this paper, we study a type of polynomial Lienard system of degree m (m >= 2) with polynomial perturbations of degree n. We prove that the first order Melnikov function of such system has at most n + 1 - [n+1/m+1] independent perturbation parameters which can be used to simplify this kind of systems. As an application, we study a type of Lienard systems for m = 4, n = 19, 28 and obtain the new lower bounds of the maximal number of limit cycles. (C) 2018 Published by Elsevier Inc.

【 授权许可】

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