ON THE NUMBER AND DISTRIBUTIONS OF LIMIT CYCLES IN A QUINTIC PLANAR VECTOR FIELD

被引：12

作者：

Wu Yuhai ^{[1
]}

Gao, Yongxi ^{[1
]}

Han, Maoan ^{[2
]}

机构：

[1] Jiang Su Univ, Dept Math, Zhenjiang 212013, Peoples R China

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

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2008年 / 18卷 / 07期

关键词：

Double homoclinic loops; Melnikov function; stability; bifurcation; limit cycles; distributions of limit cycles;

D O I：

10.1142/S0218127408021464

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper is concerned with the number and distributions of limit cycles in a Z(2)-equivariant quintic planar vector field. By applying qualitative analysis method of differential equation, we find that 28 limit cycles with four different configurations appear in this special planar polynomial system. It is concluded that H(5) >= 28 = 5(2) + 3, where H(5) is the Hilbert number for quintic polynomial systems. The results obtained are useful to the study of the second part of 16th Hilbert problem.

引用

页码：1939 / 1955

页数：17

共 19 条

[1] [Anonymous], PERIODIC SOLUTION DY
[2] [Anonymous], 1986, TRANSLATIONS MATH MO
[3] An explicit expression of the first Liapunov and period constants with applications
Gasull, A
Guillamon, A
Manosa, V
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1997, 211 (01) : 190 - 212
[4] On the number of limit cycles in double homoclinic bifurcations
Han, M
Chen, J
[J]. SCIENCE IN CHINA SERIES A-MATHEMATICS PHYSICS ASTRONOMY, 2000, 43 (09): : 914 - 928
[5] Han M, 2005, DISCRETE CONT DYN-A, V12, P675
[6] On the stability of double homoclinic and heteroclinic cycles
Han, M
Hu, SC
Liu, XB
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2003, 53 (05) : 701 - 713
[7] The stability of double homoclinic loops
Han, MA
Wu, YH
[J]. APPLIED MATHEMATICS LETTERS, 2004, 17 (11) : 1291 - 1298
[8] Bifurcation of limit cycles near polycycles with n vertices
Han, MA
Wu, YH
Bi, P
[J]. CHAOS SOLITONS & FRACTALS, 2004, 22 (02) : 383 - 394
[9] Han MA, 1999, J DIFFER EQUATIONS, V155, P245
[10] Bifurcation of limit cycles in a fourth-order near-Hamiltonian system
Han, Maoan
Shang, Desheng
Zheng, Wang
Yu, Pei
[J]. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2007, 17 (11): : 4117 - 4144

← 1 2 →