Periodic Orbits Bifurcating from a Nonisolated Zero-Hopf Equilibrium of Three-Dimensional Differential Systems Revisited

被引：1

作者：

Candido, Murilo R. ^{[1
]}

Llibre, Jaume ^{[1
]}

机构：

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

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2018年 / 28卷 / 05期

关键词：

Averaging theory; periodic solutions; polynomial differential systems; zero-Hopf bifurcation; zero-Hopf equilibrium;

D O I：

10.1142/S021812741850058X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study the periodic solutions bifurcating from a nonisolated zero-Hopf equilibrium in a polynomial differential system of degree two in R-3. More specifically, we use recent results of averaging theory to improve the conditions for the existence of one or two periodic solutions bifurcating from such a zero-Hopf equilibrium. This new result is applied for studying the periodic solutions of differential systems in R-3 having n-scroll chaotic attractors.

引用

页数：11

共 47 条

[1] LIMIT CYCLES BIFURCATING FROM A NON-ISOLATED ZERO-HOPF EQUILIBRIUM OF THREE-DIMENSIONAL DIFFERENTIAL SYSTEMS
Llibre, Jaume
Xiao, Dongmei
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2014, 142 (06) : 2047 - 2062
[2] 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
[3] Zero-Hopf Periodic Orbits for a Rossler Differential System
Llibre, Jaume
Makhlouf, Ammar
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2020, 30 (12):
[4] Small Amplitude Periodic Orbits in Three-Dimensional Quadratic Vector Fields with a Zero-Hopf Singularity
Garcia, Isaac A.
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2024, 36 (02) : 1325 - 1346
[5] Zero-Hopf Bifurcations in Three-Dimensional Chaotic Systems with One Stable Equilibrium
Ibre, Jaume
Messias, Marcelo
Reinol, Alisson de Carvalho
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2020, 30 (13):
[6] 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
[7] Integrable zero-Hopf singularities and three-dimensional centres
Garcia, Isaac A.
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2018, 148 (02) : 327 - 340
[8] THE THREE-DIMENSIONAL CENTER PROBLEM FOR THE ZERO-HOPF SINGULARITY
Garcia, Isaac A.
Valls, Claudia
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2016, 36 (04) : 2027 - 2046
[9] Periodic orbits bifurcating from a Hopf equilibrium of 2-dimensional polynomial Kolmogorov systems of arbitrary degree
Djedid, Djamila
Llibre, Jaume
Makhlouf, Amar
CHAOS SOLITONS & FRACTALS, 2021, 142
[10] Periodic Orbits for a Three-Dimensional Biological Differential Systems
Colucci, Renato
Nunez, Daniel
ABSTRACT AND APPLIED ANALYSIS, 2013,

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