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

[1] Four-dimensional Zero-Hopf Bifurcation of Quadratic Polynomial Differential System, via Averaging Theory of Third Order
Djamila Djedid
El Ouahma Bendib
Amar Makhlouf
Journal of Dynamical and Control Systems, 2022, 28 : 901 - 916
[2] N-Dimensional Zero-Hopf Bifurcation of Polynomial Differential Systems via Averaging Theory of Second Order
Kassa, S.
Llibre, J.
Makhlouf, A.
JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS, 2021, 27 (02) : 283 - 291
[3] N-Dimensional Zero-Hopf Bifurcation of Polynomial Differential Systems via Averaging Theory of Second Order
S. Kassa
J. Llibre
A. Makhlouf
Journal of Dynamical and Control Systems, 2021, 27 : 283 - 291
[4] Zero-Hopf bifurcation of a cubic jerk system via the third order averaging method
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MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2025, 48 (03) : 3595 - 3604
[5] The zero-Hopf bifurcations of a four-dimensional hyperchaotic system
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JOURNAL OF MATHEMATICAL PHYSICS, 2021, 62 (05)
[6] 4-dimensional zero-Hopf bifurcation for polynomial differentials systems with cubic homogeneous nonlinearities via averaging theory
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[7] Zero-Hopf Polynomial Centers of Third-Order Differential Equations
Garcia, Isaac A.
Valls, Claudia
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2018, 30 (02) : 557 - 578
[8] Zero-Hopf Polynomial Centers of Third-Order Differential Equations
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Journal of Dynamics and Differential Equations, 2018, 30 : 557 - 578
[9] On the 3-dimensional Hopf bifurcation via averaging theory of third order
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Badi, Sabrina
Makhlouf, Amar
TURKISH JOURNAL OF MATHEMATICS, 2017, 41 (04) : 1053 - +
[10] 3-Dimensional zero–Hopf bifurcation via averaging theory of fourth order
Achref Eddine Tabet
Amar Makhlouf
Sara Kassa
São Paulo Journal of Mathematical Sciences, 2025, 19 (1)

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