BIFURCATION OF LIMIT CYCLE AT THE INFINITY ON A CENTER MANIFOLDS IN SPACE VECTOR FIELD

被引：0

作者：

Du, Chaoxiong ^{[1
]}

Huang, Wentao ^{[2
]}

机构：

[1] Changsha Normal Univ, Sch Math Sci, Changsha 410100, Hunan, Peoples R China

[2] Guangxi Normal Univ, Coll Math & Stat, Guilin 541006, Guangxi, Peoples R China

来源：

JOURNAL OF APPLIED ANALYSIS AND COMPUTATION | 2024年 / 14卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Space vector field; infinity; limit cycle bifurcation; focal values; SINGULAR POINT; HOPF-BIFURCATION; SYSTEMS;

D O I：

10.11948/20230254

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we deal with the problem of large amplitude limit cycles bifurcation at infinity in space vector field. By making two appropriate transformations and making use of singular values methods on a center manifold to compute focal values carefully, we obtain the simplified expressions of the first five focal values at the infinity by using symbolic calculation methods. Further, we show the infinity can bifurcate 5 large limit cycles.

引用

页码：408 / 423

页数：16

共 50 条

[21] Bifurcation from infinity of the Schrodinger equation via invariant manifolds
Li, Chunqiu
Wang, Jintao
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2021, 213
[22] HOPF BIFURCATION AT INFINITY AND DISSIPATIVE VECTOR FIELDS OF THE PLANE
Alarcon, Begona
Rabanal, Roland
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2017, 145 (07) : 3033 - 3046
[23] Limit cycle and bifurcation of nonlinear problems
He, JH
CHAOS SOLITONS & FRACTALS, 2005, 26 (03) : 827 - 833
[24] EIGENVALUES, BIFURCATION, AND CENTER MANIFOLDS IN THE PRESENCE OF NOISE
ARNOLD, L
BOXLER, P
DIFFERENTIAL EQUATIONS //: PROCEEDINGS OF THE EQUADIFF CONFERENCE, 1989, 118 : 33 - 48
[25] SMOOTH NORMALIZATION OF A VECTOR FIELD NEAR A SEMISTABLE LIMIT-CYCLE
YAKOVENKO, SY
ANNALES DE L INSTITUT FOURIER, 1993, 43 (03) : 893 - 903
[26] A Data Driven Vector Field Oscillator with Arbitrary Limit Cycle Shape
Pasandi, Venus
Dinale, Aiko
Keshmiri, Mehdi
Pucci, Daniele
2019 IEEE 58TH CONFERENCE ON DECISION AND CONTROL (CDC), 2019, : 8007 - 8012
[27] Bifurcation at infinity for equations in spaces of vector-valued functions
Diamond, P
Kloeden, PE
Krasnoselskii, AM
Pokrovskii, AV
JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS, 1997, 63 : 263 - 280
[28] Bifurcation and Isochronicity at Infinity in a Class of Cubic Polynomial Vector Fields
Qin-long Wang Department of Information and Mathematics
Acta Mathematicae Applicatae Sinica, 2007, (03) : 451 - 466
[29] Bifurcation and isochronicity at infinity in a class of cubic polynomial vector fields
Wang, Qin-long
Liu, Yi-rong
ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES, 2007, 23 (03): : 451 - 466
[30] BIFURCATION OF VECTOR FIELD SINGULARITIES
TEIXEIRA, MA
ANAIS DA ACADEMIA BRASILEIRA DE CIENCIAS, 1975, 47 (3-4): : 570 - 570

← 1 2 3 4 5 →