The Cubic Polynomial Differential Systems with two Circles as Algebraic Limit Cycles

被引：3

作者：

Gine, Jaume ^{[1
]}

Llibre, Jaume ^{[2
]}

Valls, Claudia ^{[3
]}

机构：

[1] Univ Lleida, Dept Matemat, Avda Jaume 2 69, Lleida 25001, Catalonia, Spain

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

[3] Univ Lisbon, Inst Super Tecn, Dept Matemat, Av Rovisco Pais, P-1049001 Lisbon, Portugal

来源：

ADVANCED NONLINEAR STUDIES | 2018年 / 18卷 / 01期

关键词：

Cubic Systems; Limit Cycles; Invariant Algebraic Curves; 16TH HILBERT PROBLEM; INTEGRABILITY;

D O I：

10.1515/ans-2017-6033

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we characterize all cubic polynomial differential systems in the plane having two circles as invariant algebraic limit cycles.

引用

页码：183 / 193

页数：11

共 50 条

[31] NEW FAMILIES OF CENTERS AND LIMIT CYCLES FOR POLYNOMIAL DIFFERENTIAL SYSTEMS WITH HOMOGENEOUS NONLINEARITIES
李承治
李伟固
Jaume Llibre
张芷芬
Annals of Differential Equations, 2003, (03) : 302 - 317
[32] ON A CLASS OF POLYNOMIAL DIFFERENTIAL SYSTEMS OF DEGREE 4: PHASE PORTRAITS AND LIMIT CYCLES
Llibre, Jaume
Salhi, Tayeb
TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, 2021, 57 (02) : 441 - 463
[33] Two Limit Cycles in Lienard Piecewise Linear Differential Systems
Llibre, Jaume
Ponce, Enrique
Valls, Claudia
JOURNAL OF NONLINEAR SCIENCE, 2019, 29 (04) : 1499 - 1522
[34] Limit cycles for discontinuous quadratic differential systems with two zones
Llibre, Jaume
Mereu, Ana C.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2014, 413 (02) : 763 - 775
[35] The number of limit cycles for a family of polynomial systems
Xiang, GH
Han, MA
Zhang, TH
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2005, 49 (11-12) : 1669 - 1678
[36] The non-existence, existence and uniqueness of limit cycles for quadratic polynomial differential systems
Llibre, Jaume
Zhang, Xiang
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2019, 149 (01) : 1 - 14
[37] LIMIT CYCLES FOR A CLASS OF GENERALIZED LIENARD POLYNOMIAL DIFFERENTIAL SYSTEMS VIA AVERAGING THEORY
Kina, A.
Berbache, A.
Bendjeddou, A.
ACTA MATHEMATICA UNIVERSITATIS COMENIANAE, 2021, 90 (04): : 437 - 455
[38] Limit cycles of polynomial differential systems bifurcating from the periodic orbits of a linear differential system in Rd
Llibre, Jaume
Makhlouf, Amar
BULLETIN DES SCIENCES MATHEMATIQUES, 2009, 133 (06): : 578 - 587
[39] Coexistence of Algebraic Limit Cycles and Small Limit Cycles of Two Classes of Near-Hamiltonian Systems with a Nilpotent Singular Point
Liu, Huimei
Cai, Meilan
Li, Feng
AXIOMS, 2024, 13 (09)
[40] Two Limit Cycles in Liénard Piecewise Linear Differential Systems
Jaume Llibre
Enrique Ponce
Clàudia Valls
Journal of Nonlinear Science, 2019, 29 : 1499 - 1522

← 1 2 3 4 5 →