Bifurcation of limit cycles from a Liénard system with a heteroclinic loop connecting two nilpotent saddles

被引：0
作者：
Xianbo Sun
机构：
[1] Guangxi University of Finance and Economics,Department of Information and Statistics
来源：
Nonlinear Dynamics | 2013年 / 73卷
关键词：
Melnikov function; Heteroclinic loop; Nilpotent saddle; Limit cycle; Bifurcation;
D O I：
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学科分类号：
摘要：
In this article, we study the limit cycles bifurcated from a Liénard system with a heteroclinic loop connecting two nilpotent saddles. We apply expansion theory of a first-order Melnikov function to investigate the number of limit cycles near the heteroclinic loop and the center, and by some perturbation theory we find 3 limit cycles with 7 different distributions. Last, the least upper bound of the number of limit cycles bifurcated from the annulus is given by an algebraic criterion developed in J. Differ. Equ. 251, 1656–1669 (2011).
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页码：869 / 880
页数：11
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