Higher Order Melnikov Functions for Studying Limit Cycles of Some Perturbed Elliptic Hamiltonian Vector Fields

被引：4

作者：

Asheghi, Rasoul ^{[1
]}

Nabavi, Arefeh ^{[1
]}

机构：

[1] Isfahan Univ Technol, Dept Math Sci, Esfahan 8415683111, Iran

来源：

QUALITATIVE THEORY OF DYNAMICAL SYSTEMS | 2019年 / 18卷 / 01期

关键词：

Limit cycles; Hamiltonian systems; Melnikov functions;

D O I：

10.1007/s12346-018-0284-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the number of limit cycles in the perturbed Hamiltonian system dH=epsilon F1+epsilon 2F2+epsilon 3F3 with Fi, the vector valued homogeneous polynomials of degree i and 4-i for i=1,2,3, and small positive parameter epsilon. The Hamiltonian function has the form H=y2/2+U(x), where U is a univariate polynomial of degree four without symmetry. We compute higher order Melnikov functions until we obtain reversible perturbations. Then we find the upper bounds for the number of limit cycles that can bifurcate from the periodic orbits of dH=0.

引用

页码：289 / 313

页数：25

共 38 条

[1] Higher Order Melnikov Functions for Studying Limit Cycles of Some Perturbed Elliptic Hamiltonian Vector Fields
Rasoul Asheghi
Arefeh Nabavi
[J]. Qualitative Theory of Dynamical Systems, 2019, 18 : 289 - 313
[2] THE NUMBER OF LIMIT CYCLES FROM ELLIPTIC HAMILTONIAN VECTOR FIELDS BY HIGHER ORDER MELNIKOV FUNCTIONS
Liu, Xia
[J]. JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2023, 13 (03): : 1239 - 1254
[3] Using Melnikov functions of any order for studying limit cycles
Tigan, Gheorghe
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2017, 448 (01) : 409 - 420
[4] Bifurcation theory of limit cycles by higher order Melnikov functions and applications
Liu, Shanshan
Han, Maoan
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2024, 403 : 29 - 66
[5] Limit cycles bifurcated from piecewise Hamiltonian systems by Melnikov functions of any order
Yang, Peixing
Yu, Jiang
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2024, 404 : 108 - 129
[6] THE NUMBER OF LIMIT CYCLES FROM A QUARTIC CENTER BY THE HIGHER-ORDER MELNIKOV FUNCTIONS
Liu, Xia
[J]. JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2021, 11 (03): : 1405 - 1421
[7] Fourteen limit cycles in a cubic Hamiltonian system with higher-order perturbed terms
Hong, XC
Liu, ZR
[J]. PROCEEDINGS OF THE 4TH INTERNATIONAL CONFERENCE ON NONLINEAR MECHANICS, 2002, : 1211 - 1215
[8] Heteroclinic bifurcation of limit cycles in perturbed cubic Hamiltonian systems by higher-order analysis
Geng, Wei
Han, Maoan
Tian, Yun
Ke, Ai
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2023, 357 : 412 - 435
[9] Thirteen limit cycles for a class of cubic Hamiltonian system with higher-order perturbed terms
Zhou, Hongxian
Xu, Wei
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2008, 204 (02) : 905 - 913
[10] On the number of limit cycles for some perturbed Hamiltonian polynomial systems
Llibre, J
Zhang, X
[J]. DYNAMICS OF CONTINUOUS DISCRETE AND IMPULSIVE SYSTEMS-SERIES A-MATHEMATICAL ANALYSIS, 2001, 8 (02): : 161 - 181

← 1 2 3 4 →