On the Hopf-zero bifurcation of the Michelson system

被引：21

作者：

Llibre, Jaume ^{[1
]}

Zhang, Xiang ^{[2
]}

机构：

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

[2] Shanghai Jiao Tong Univ, Dept Math, Shanghai 200240, Peoples R China

来源：

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2011年 / 12卷 / 03期

关键词：

Michelson system; Periodic orbit; Averaging method; Hopf bifurcation; STEADY SOLUTIONS;

D O I：

10.1016/j.nonrwa.2010.10.019

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Applying a new result for studying the periodic orbits of a differential system via the averaging theory, we provide the first analytic proof of the existence of a Hopf-zero bifurcation for the Michelson system (x) over dot = y, (y) over dot = z, (z) over dot = c(2) - y - x(2)/2, at c = 0. Moreover our method estimates the shape of this periodic orbit as a function of c > 0, sufficiently small. (C) 2010 Elsevier Ltd. All rights reserved.

引用

页码：1650 / 1653

页数：4

共 50 条

[1] Hypernormal form for the Hopf-zero bifurcation
Algaba, A
Freire, E
Gamero, E
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 1998, 8 (10): : 1857 - 1887
[2] Zero-Hopf bifurcation in the generalized Michelson system
Llibre, Jaume
Makhlouf, Amar
CHAOS SOLITONS & FRACTALS, 2016, 89 : 228 - 231
[3] Hopf-zero bifurcation of Oregonator oscillator with delay
Cai, Yuting
Liu, Liqin
Zhang, Chunrui
ADVANCES IN DIFFERENCE EQUATIONS, 2018,
[4] Hopf-zero bifurcation of Oregonator oscillator with delay
Yuting Cai
Liqin Liu
Chunrui Zhang
Advances in Difference Equations, 2018
[5] Hopf-zero bifurcation in a generalized Gopalsamy neural network model
Ding, Yuting
Jiang, Weihua
Yu, Pei
NONLINEAR DYNAMICS, 2012, 70 (02) : 1037 - 1050
[6] Hopf-zero bifurcation in a generalized Gopalsamy neural network model
Yuting Ding
Weihua Jiang
Pei Yu
Nonlinear Dynamics, 2012, 70 : 1037 - 1050
[7] Piecewise Linear Analogue of Hopf-Zero Bifurcation in an Extended BVP Oscillator
Ponce, Enrique
Ros, Javier
Vela, Elisabet
ADVANCES IN DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2014, 4 : 113 - 121
[8] Hopf-zero bifurcation of the ring unidirectionally coupled Toda oscillators with delay
Su, Rina
Zhang, Chunrui
NONLINEAR ANALYSIS-MODELLING AND CONTROL, 2021, 26 (03): : 375 - 395
[9] Bifurcation Control and Universal Unfolding for Hopf-Zero Singularities with Leading Solenoidal Terms
Gazor, Majid
Sadri, Nasrin
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, 2016, 15 (02): : 870 - 903
[10] HOPF-ZERO BIFURCATION OF A DELAYED PREDATOR-PREY MODEL WITH DORMANCY OF PREDATORS
Wang, Jingnan
Jiang, Weihua
JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2017, 7 (03): : 1051 - 1069

← 1 2 3 4 5 →