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
收藏
页数:13
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