Zero-Hopf bifurcation in the generalized Michelson system

被引：13
|
作者：
Llibre, Jaume [1 ]
Makhlouf, Amar [2 ]
机构：
[1] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Catalonia, Spain
[2] Univ Annaba, Lab LMA, Dept Math, Elhadjar 23, Annaba, Algeria
来源：
CHAOS SOLITONS & FRACTALS | 2016年 / 89卷
关键词：
Periodic solution; Averaging theory; Zero-Hopf Bifurcation; Michelson system; Triple-zero bifurcation; ANALYTIC UNFOLDINGS; SINGULARITY;
D O I：
10.1016/j.chaos.2015.11.013
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We provide sufficient conditions for the existence of two periodic solutions bifurcating from a zero-Hopf equilibrium for the differential system (x) over dot = y, (y) over dot = z , (z) over dot = a+by+cz -x(2)/2, where a, b and c are real arbitrary parameters. The regular perturbation of this differential system provides the normal form of the so-called triple-zero bifurcation. (C) 2015 Elsevier Ltd. All rights reserved.
引用
收藏
页码：228 / 231
页数：4
相关论文
共 50 条
  • [31] Transcritical and zero-Hopf bifurcations in the Genesio system
    Pedro Toniol Cardin
    Jaume Llibre
    [J]. Nonlinear Dynamics, 2017, 88 : 547 - 553
  • [32] Zero-Hopf bifurcation analysis in delayed differential equations with two delays
    Wu, Xiaoqin P.
    Wang, Liancheng
    [J]. JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 2017, 354 (03): : 1484 - 1513
  • [33] Zero-Hopf bifurcation analysis in an inertial two-neural system with delayed Crespi function
    Yingying Li
    Li Xiao
    Zhouchao Wei
    Wei Zhang
    [J]. The European Physical Journal Special Topics, 2020, 229 : 953 - 962
  • [34] Zero-Hopf bifurcation analysis in an inertial two-neural system with delayed Crespi function
    Li, Yingying
    Xiao, Li
    Wei, Zhouchao
    Zhang, Wei
    [J]. EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS, 2020, 229 (6-7): : 953 - 962
  • [35] Zero-Hopf bifurcation for van der Pol's oscillator with delayed feedback
    Wu, Xiaoqin
    Wang, Liancheng
    [J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2011, 235 (08) : 2586 - 2602
  • [36] Zero-Hopf bifurcation in continuous dynamical systems using multiple scale approach
    Al-khedhairi, A.
    Askar, S. S.
    Elsonbaty, A.
    Elsadany, A. A.
    [J]. AIN SHAMS ENGINEERING JOURNAL, 2020, 11 (04) : 1377 - 1385
  • [37] The Integrability and the Zero-Hopf Bifurcation of the Three Dimensional Lotka-Volterra Systems
    Salih, Rizgar H.
    [J]. 6TH INTERNATIONAL EURASIAN CONFERENCE ON MATHEMATICAL SCIENCES AND APPLICATIONS (IECMSA-2017), 2018, 1926
  • [38] Zero-Hopf Periodic Orbits for a Rossler Differential System
    Llibre, Jaume
    Makhlouf, Ammar
    [J]. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2020, 30 (12):
  • [39] On the Zero-Hopf Bifurcation of the Lotka-Volterra Systems in R3
    Han, Maoan
    Llibre, Jaume
    Tian, Yun
    [J]. MATHEMATICS, 2020, 8 (07)
  • [40] Zero-Hopf Bifurcation of a memristive synaptic Hopfield neural network with time delay
    Dong, Tao
    Gong, Xiaomei
    Huang, Tingwen
    [J]. NEURAL NETWORKS, 2022, 149 : 146 - 156
12345