Algebraic Limit Cycle of Degree 2 for Linear Type Center Plus Cubic Homogeneous Polynomial Differential Systems

被引：0

作者：

Luping Wang ^{[1
]}

Yuzhou Tian ^{[2
]}

Yulin Zhao ^{[1
]}

机构：

[1] Wang, Luping

[2] Tian, Yuzhou

[3] Zhao, Yulin

来源：

Zhao, Yulin (mcszyl@mail.sysu.edu.cn) | 2025年 / 31卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Invariant algebraic curve; Algebraic limit cycles; Rotated vector fields; Primary: 34C07; Secondary: 34C05;

D O I：

10.1007/s10883-024-09722-z

中图分类号：

学科分类号：

摘要：

In this paper, we study the algebraic limit cycle of degree 2 for the system x˙=-y+a30x3+a21x2y+a12xy2+a03y3, y˙=x+b30x3+b21x2y+b12xy2+b03y3, which is called a linear type center plus cubic homogeneous polynomial differential system. We derive the normal form of this system with an algebraic limit cycle of degree 2. It is shown that, if an invariant algebraic curve of degree 2 is a limit cycle of the above mentioned system, then it is a unique limit cycle in the phase plane. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.

引用

共 50 条

[21] Limit cycles of polynomial differential systems of degree 1 and 2 on the cylinder
Johana Jimenez
Jaume Llibre
São Paulo Journal of Mathematical Sciences, 2023, 17 : 679 - 691
[22] Limit cycles of polynomial differential systems of degree 1 and 2 on the cylinder
Jimenez, Johana
Llibre, Jaume
SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES, 2023, 17 (02): : 679 - 691
[23] Limit cycles of polynomial differential systems with homogeneous nonlinearities of degree 4 via the averaging method
Cao, Jinlong
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2008, 220 (1-2) : 624 - 631
[24] Phase portraits of reversible linear differential systems with cubic homogeneous polynomial nonlinearities having a non-degenerate center at the origin
Buzzi C.A.
Llibre J.
Medrado J.C.R.
Qualitative Theory of Dynamical Systems, 2009, 7 (2) : 369 - 403
[25] The algebraic curves of planar polynomial differential systems with homogeneous nonlinearities
Cheresiz, Vladimir M.
Volokitin, Evgenii P.
ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2021, (51) : 1 - 12
[26] LIMIT CYCLES FOR PIECEWISE SMOOTH PERTURBATIONS OF A CUBIC POLYNOMIAL DIFFERENTIAL CENTER
Li, Shimin
Huang, Tiren
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2015,
[27] Isochronous centers of a linear center perturbed by fourth degree homogeneous polynomial
Chavarriga, J
Giné, J
García, IA
BULLETIN DES SCIENCES MATHEMATIQUES, 1999, 123 (02): : 77 - 96
[28] Bifurcations of limit circles and center conditions for a class of non-analytic cubic Z 2 polynomial differential systems
Li, Feng
Liu, Yi Rong
Jin, Yin Lai
ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2012, 28 (11) : 2275 - 2288
[29] Classification of the centers, their cyclicity and isochronicity for a class of polynomial differential systems generalizing the linear systems with cubic homogeneous nonlinearities
Llibre, Jaume
Valls, Claudia
JOURNAL OF DIFFERENTIAL EQUATIONS, 2009, 246 (06) : 2192 - 2204
[30] Hamiltonian nilpotent saddles of linear plus cubic homogeneous polynomial vector fields
Corbera, Montserrat
Valls, Claudia
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2022, 64

← 1 2 3 4 5 →