Bifurcation of limit cycles near a heteroclinic loop with nilpotent cusps

被引：0

作者：

Ma, Deyue ^{[1
]}

Yang, Junmin ^{[1
]}

机构：

[1] Hebei Normal Univ, Sch Math Sci, Shijiazhuang 050024, Hebei, Peoples R China

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2023年 / 125卷

基金：

中国国家自然科学基金;

关键词：

Melnikov function; Limit cycle; Heteroclinic loop; Nilpotent cusp; CUSPIDAL LOOP; HOPF;

D O I：

10.1016/j.cnsns.2023.107337

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the relation between the coefficients in the expansions of two Melnikov functions near a heteroclinic loop with nilpotent cusps. Based on this relation, we give a condition of obtaining limit cycles near the heteroclinic loop. Further, we present a method to compute more coefficients in the expansions of two Melnikov functions near the heteroclinic loop. As an application, we consider a class of Lienard systems and study the number of limit cycles bifurcated from a heteroclinic loop and an elementary center. & COPY; 2023 Elsevier B.V. All rights reserved.

引用

页数：13

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