Four-dimensional Zero-Hopf Bifurcation of Quadratic Polynomial Differential System, via Averaging Theory of Third Order

被引：2

作者：

Djedid, Djamila ^{[1
]}

Bendib, El Ouahma ^{[2
]}

Makhlouf, Amar ^{[1
]}

机构：

[1] Univ Annaba, Dept Math, Lab LMA, POB 12, Annaba 23000, Algeria

[2] Univ Skikda 20 August 1955, Lab LMA, Dept Math, POB 12, Annaba 23000, Algeria

来源：

JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS | 2022年 / 28卷 / 04期

关键词：

Zero-Hopf bifurcation; Averaging theory; Quadratic polynomial differential system;

D O I：

10.1007/s10883-020-09528-9

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This article concerns the zero-Hopf bifurcation of a quadratic polynomial differential system in R-4. By using the averaging theory of third order, we provide that at most 25 limit cycles can bifurcate from one singularity with eigenvalues of the form +/- bi, 0 and 0.

引用

页码：901 / 916

页数：16

共 32 条

[21] Limit Cycles of the Three-dimensional Quadratic Differential System via Hopf Bifurcation
Abddulkareem, Aram A.
Amen, Azad I.
Hussein, Niazy H.
BAGHDAD SCIENCE JOURNAL, 2024, 21 (09) : 2970 - 2983
[22] AVERAGING APPROACH TO CYCLICITY OF HOPF BIFURCATION IN PLANAR LINEAR-QUADRATIC POLYNOMIAL DISCONTINUOUS DIFFERENTIAL SYSTEMS
Chen, Xingwu
Llibre, Jaume
Zhang, Weinian
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2017, 22 (10): : 3953 - 3965
[23] Stability and Hopf bifurcation analysis of a new four-dimensional hyper-chaotic system
Zhou, Liangqiang
Zhao, Ziman
Chen, Fangqi
MODERN PHYSICS LETTERS B, 2020, 34 (29):
[24] Hopf bifurcation and intermittent transition to hyperchaos in a novel strong four-dimensional hyperchaotic system
Wu, Wenjuan
Chen, Zengqiang
NONLINEAR DYNAMICS, 2010, 60 (04) : 615 - 630
[25] Hopf bifurcation and intermittent transition to hyperchaos in a novel strong four-dimensional hyperchaotic system
Wenjuan Wu
Zengqiang Chen
Nonlinear Dynamics, 2010, 60 : 615 - 630
[26] Limit cycles bifurcating from a zero-Hopf equilibrium of a 3-dimensional continuous differential system
Sara Kassa
Jaume Llibre
Amar Makhlouf
São Paulo Journal of Mathematical Sciences, 2021, 15 : 419 - 426
[27] HOPF BIFURCATION FOR SOME ANALYTIC DIFFERENTIAL SYSTEMS IN R3 VIA AVERAGING THEORY
Llibre, Jaume
Valls, Claudia
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2011, 30 (03) : 779 - 790
[28] Limit cycles bifurcating from a zero-Hopf equilibrium of a 3-dimensional continuous differential system
Kassa, Sara
Llibre, Jaume
Makhlouf, Amar
SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES, 2021, 15 (01): : 419 - 426
[29] Hopf Bifurcation, Positively Invariant Set, and Physical Realization of a New Four-Dimensional Hyperchaotic Financial System
Kai, G.
Zhang, W.
Wei, Z. C.
Wang, J. F.
Akgul, A.
MATHEMATICAL PROBLEMS IN ENGINEERING, 2017, 2017
[30] Existence of Solutions for a System of Second-order Four-dimensional Differential Equations
Fu Meifen
Liu Xiaoyan
PROCEEDINGS OF THE 2010 INTERNATIONAL CONFERENCE ON APPLICATION OF MATHEMATICS AND PHYSICS, VOL 2: ADVANCES ON APPLIED MATHEMATICS AND COMPUTATION MATHEMATICS, 2010, : 27 - 31

← 1 2 3 4 →