EXACT BOUND ON THE NUMBER OF LIMIT CYCLES ARISING FROM A PERIODIC ANNULUS BOUNDED BY A SYMMETRIC HETEROCLINIC LOOP

被引：5

作者：

Sun, Xianbo ^{[1
,2
]}

机构：

[1] Guangxi Univ Finance & Econ, Dept Appl Math, 100 West Mingxiu, Nanning 530003, Peoples R China

[2] Western Univ, Dept Appl Math, 1151 Richmond St, London, ON N6A 5B7, Canada

来源：

JOURNAL OF APPLIED ANALYSIS AND COMPUTATION | 2020年 / 10卷 / 01期

基金：

中国国家自然科学基金; 美国国家科学基金会;

关键词：

Limit cycle; Abelian integral; heteroclinic loop; sharp bound; ELLIPTIC HAMILTONIAN-SYSTEMS; BIFURCATION; PERTURBATIONS; DEGREE-4; SADDLE; ZEROS; HOPF;

D O I：

10.11948/20190294

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the bound on the number of limit cycles by Poincare bifurcation in a small perturbation of some seventh-degree Hamiltonian system is concerned. The lower and upper bounds on the number of limit cycles have been obtained in two previous works, however, the sharp bound is still unknown. We will employ some new techniques to determine which is the exact bound between 3 and 4. The asymptotic expansions are used to determine the four vertexes of a tetrahedron, and the sharp bound can be reached when the parameters belong to this tetrahedron.

引用

页码：378 / 390

页数：13

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