On Double Homoclinic Bifurcation of Limit Cycles in Near-Hamiltonian Systems on the Cylinder

被引：0

作者：

Ke, Ai ^{[1
]}

Yang, Junmin ^{[2
]}

机构：

[1] Zhejiang Normal Univ, Sch Math Sci, Jinhua 321004, Peoples R China

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

来源：

QUALITATIVE THEORY OF DYNAMICAL SYSTEMS | 2024年 / 23卷 / 05期

基金：

中国国家自然科学基金;

关键词：

Limit cycle; Melnikov function; Homoclinic loop; NUMBER; EQUATION; SMOOTH;

D O I：

10.1007/s12346-024-01107-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the bifurcation problem of limit cycles in near-Hamiltonian systems near a double homoclinic loop on the cylinder. We obtain a sufficient condition to find a lower bound of the maximal number of limit cycles near the loop by the coefficients of the expansions of the three Melnikov functions corresponding to the three families of periodic orbits near the double homoclinic loop. We also provide an application of our main results to a class of cylindrical systems.

引用

页数：20

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