Bifurcation of limit cycles near heteroclinic loops in near-Hamiltonian systems

被引：14

作者：

Geng, Wei ^{[1
]}

Tian, Yun ^{[1
]}

机构：

[1] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2021年 / 95卷

基金：

中国国家自然科学基金;

关键词：

Limit cycles; Bifurcation; Heteroclinic loops; Melnikov function; Asymptotic expansion; NUMBER; POINT;

D O I：

10.1016/j.cnsns.2020.105666

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the bifurcation of limit cycles near a heterocilinc loop with hyperbolic saddles in a perturbed planar Hamiltonian system. We present a method for computing the coefficients in the corresponding expansion of the first order Melnikov function. With more those coefficients, more limit cycles could be determined around the heteroclinic loop. An example of studying limit cycles produced from a heteroclinic loop with 2 saddles is investigated to illustrate our method. (C) 2020 Elsevier B.V. All rights reserved.

引用

页数：10

共 24 条

[1]

Arnold V.I., 1977, Funct. Anal. Appl., V11, P85, DOI DOI 10.1007/BF01081886

[2] Bifurcation of Limit Cycles in a Near-Hamiltonian System with a Cusp of Order Two and a Saddle [J].

Bakhshalizadeh, Ali ;

Zangeneh, Hamid R. Z. ;

Kazemi, Rasool .

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2016, 26 (11)

[3]

Christopher C, 2005, TRENDS MATH, P23

[4]

Christopher C., 2007, LIMIT CYCLES DIFFERE

[5] Perturbations of quadratic Hamiltonian two-saddle cycles [J].

Gavrilov, Lubomir ;

They, Iliya D. .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2015, 32 (02) :307-324

[6] On the number of limit cycles which appear by perturbation of two-saddle cycles of planar vector fields [J].

Gavrilov, Lubomir .

FUNCTIONAL ANALYSIS AND ITS APPLICATIONS, 2013, 47 (03) :174-186

[7] Higher order limit cycle bifurcations from non-degenerate centers [J].

Gine, Jaume .

APPLIED MATHEMATICS AND COMPUTATION, 2012, 218 (17) :8853-8860

[8]

Han M., 2013, Bifurcation Theory of Limit Cycles

[9]

HAN MA, 1994, SCI CHINA SER A, V37, P1325

[10] Limit Cycles Near Homoclinic and Heteroclinic Loops [J].

Han, Maoan ;

Yang, Junmin ;

Tarta, Alexandrina -Alina ;

Gao, Yang .

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2008, 20 (04) :923-944

← 1 2 3 →