Limit cycles for a class of three-dimensional polynomial differential systems

被引：5

作者：

Llibre, Jaume ^{[1
]}

Yu, Jiang

机构：

[1] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Spain

[2] Shanghai Jiao Tong Univ, Dept Math, Shanghai 200240, Peoples R China

来源：

JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS | 2007年 / 13卷 / 04期

关键词：

linear center; limit cycle; averaging theory; polynomial differential system;

D O I：

10.1007/s10883-007-9025-5

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

Perturbing the system x = -y(1+x), y = x(l+x), z = 0 inside the family of polynomial differential systems of degree n in R-3, we obtain at most n(2) limit cycles using the first-order averaging theory. Moreover, there exist such perturbed systems having at least n(2) limit cycles.

引用

页码：531 / 539

页数：9

共 50 条

[21] Darboux integrability and algebraic limit cycles for a class of polynomial differential systems
Cao JinLong
Llibre, Jaume
Zhang Xiang
SCIENCE CHINA-MATHEMATICS, 2014, 57 (04) : 775 - 794
[22] Limit Cycles for a Class of Polynomial Differential Systems Via Averaging Theory
Bendjeddou, Ahmed
Berbache, Aziza
Kina, Abdelkrim
JOURNAL OF SIBERIAN FEDERAL UNIVERSITY-MATHEMATICS & PHYSICS, 2019, 12 (02): : 145 - 159
[23] Multiple Limit Cycles Bifurcation From the Degenerate Singularity for a Class of Three-dimensional Systems
Qin-long WANG
Wen-tao HUANG
Yi-rong LIU
ActaMathematicaeApplicataeSinica, 2016, 32 (01) : 73 - 80
[24] Multiple limit cycles bifurcation from the degenerate singularity for a class of three-dimensional systems
Qin-long Wang
Wen-tao Huang
Yi-rong Liu
Acta Mathematicae Applicatae Sinica, English Series, 2016, 32 : 73 - 80
[25] Multiple Limit Cycles Bifurcation From the Degenerate Singularity for a Class of Three-dimensional Systems
Wang, Qin-long
Huang, Wen-tao
Liu, Yi-rong
ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES, 2016, 32 (01): : 73 - 80
[26] Algebraic determination of limit cycles in a family of three-dimensional piecewise linear differential systems
Llibre, Jaume
Ponce, Enrique
Ros, Javier
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (17) : 6712 - 6727
[27] LIMIT CYCLES FOR A CLASS OF POLYNOMIAL SYSTEMS AND APPLICATIONS
Feng, Hanying
Xu, Rui
Liu, Qiming
Yang, Pinghua
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2003,
[28] LIMIT-CYCLES OF A CLASS OF POLYNOMIAL SYSTEMS
CARBONELL, M
LLIBRE, J
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1988, 109 : 187 - 199
[29] NORMAL FORMS AND HYPERBOLIC ALGEBRAIC LIMIT CYCLES FOR A CLASS OF POLYNOMIAL DIFFERENTIAL SYSTEMS
Llibre, Jaume
Valls, Claudia
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2018,
[30] Polynomial differential systems with hyperbolic limit cycles
Llibre, Jaume
Valls, Claudia
JOURNAL OF GEOMETRY AND PHYSICS, 2023, 194

← 1 2 3 4 5 →