A cubic system with twelve small amplitude limit cycles

被引：38

作者：

Liu, YR

Huang, WT ^{[1
]}

机构：

[1] Guilin Univ Elect Technol, Dept Comp Sci & Math, Guilin 541004, Guangxi, Peoples R China

[2] Cent S Univ, Coll Math Sci & Comp Technol, Changsha 410083, Peoples R China

来源：

BULLETIN DES SCIENCES MATHEMATIQUES | 2005年 / 129卷 / 02期

基金：

中国国家自然科学基金;

关键词：

limit cycle; focal value; singular point value; Poincard succession function;

D O I：

10.1016/j.bulsci.2004.05.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the bifurcation of limit cycles for a cubic polynomial system is investigated. By the computation of the singular point values, we prove that the system has 12 small amplitude limit cycles. The process of the proof is algebraic and symbolic. (C) 2004 Elsevier SAS. All rights reserved.

引用

页码：83 / 98

页数：16

共 50 条

[41] Coexistence of small and large amplitude limit cycles of polynomial differential systems of degree four
Eduardo Sáez
Eduardo Stange
Iván Szántó
Czechoslovak Mathematical Journal, 2007, 57 : 105 - 114
[42] Conditions for origin to be a center and the bifurcation of limit cycles in a class of cubic systems
Zhu, JH
Zhu, SM
CHINESE SCIENCE BULLETIN, 1997, 42 (14): : 1157 - 1161
[43] Conditions for origin to be a center and the bifurcation of limit cycles in a class of cubic systems
ZHU Jiehua and ZHU SimingDepartment of Mathematics
Chinese Science Bulletin, 1997, (14) : 1157 - 1161
[44] Maximum Number of Small Limit Cycles in Some Rational Lienard Systems with Cubic Restoring Terms
Chen, Jiayi
Tian, Yun
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2021, 31 (12):
[45] Self-Sustained Oscillations and Limit Cycles in the Rayleigh System with Cubic Return Force
Kumakshev, S. A.
MECHANICS OF SOLIDS, 2023, 58 (08) : 2764 - 2769
[46] Self-Sustained Oscillations and Limit Cycles in the Rayleigh System with Cubic Return Force
S. A. Kumakshev
Mechanics of Solids, 2023, 58 : 2764 - 2769
[47] Bifurcation of limit cycles for a class of cubic polynomial system having a nilpotent singular point
Pan, Xuejun
APPLIED MATHEMATICS AND COMPUTATION, 2011, 218 (04) : 1161 - 1165
[48] Bifurcations of limit cycles from infinity for a class of quintic polynomial system
Huang, W
Liu, Y
BULLETIN DES SCIENCES MATHEMATIQUES, 2004, 128 (04): : 291 - 302
[49] Limit Cycles and Integrability of a Class of Quintic System
Tang, Yanli
Zhang, Dongmei
Li, Feng
MATHEMATICS, 2022, 10 (16)
[50] Nine limit cycles around a singular point by perturbing a cubic Hamiltonian system with a nilpotent center
Yang, Junmin
Yu, Pei
APPLIED MATHEMATICS AND COMPUTATION, 2017, 298 : 141 - 152

← 1 2 3 4 5 →