On the Hopf-zero bifurcation of the Michelson system

Jaume Llibre; Xiang Zhang

doi:https://doi.org/10.1016/j.nonrwa.2010.10.019

On the Hopf-zero bifurcation of the Michelson system

Jaume Llibre, Xiang Zhang

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

22 Citations (Scopus)

Abstract

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=y,y=z,z= c2-y-x22, at c=0. Moreover our method estimates the shape of this periodic orbit as a function of c>0, sufficiently small. © 2010 Elsevier Ltd. All rights reserved.

Original language	English
Pages (from-to)	1650-1653
Journal	Nonlinear Analysis: Real World Applications
Volume	12
DOIs	https://doi.org/10.1016/j.nonrwa.2010.10.019
Publication status	Published - 1 Jun 2011

Keywords

Averaging method
Hopf bifurcation
Michelson system
Periodic orbit

Access to Document

https://doi.org/10.1016/j.nonrwa.2010.10.019

https://ddd.uab.cat/record/150468

Cite this

@article{7e2795ea32ec49b4a06d658a9b8b535d,

title = "On the Hopf-zero bifurcation of the Michelson system",

abstract = "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=y,y=z,z= c2-y-x22, at c=0. Moreover our method estimates the shape of this periodic orbit as a function of c>0, sufficiently small. {\textcopyright} 2010 Elsevier Ltd. All rights reserved.",

keywords = "Averaging method, Hopf bifurcation, Michelson system, Periodic orbit",

author = "Jaume Llibre and Xiang Zhang",

year = "2011",

month = jun,

day = "1",

doi = "https://doi.org/10.1016/j.nonrwa.2010.10.019",

language = "English",

volume = "12",

pages = "1650--1653",

journal = "Nonlinear Analysis: Real World Applications",

issn = "1468-1218",

publisher = "Elsevier BV",

}

TY - JOUR

T1 - On the Hopf-zero bifurcation of the Michelson system

AU - Llibre, Jaume

AU - Zhang, Xiang

PY - 2011/6/1

Y1 - 2011/6/1

N2 - 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=y,y=z,z= c2-y-x22, at c=0. Moreover our method estimates the shape of this periodic orbit as a function of c>0, sufficiently small. © 2010 Elsevier Ltd. All rights reserved.

AB - 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=y,y=z,z= c2-y-x22, at c=0. Moreover our method estimates the shape of this periodic orbit as a function of c>0, sufficiently small. © 2010 Elsevier Ltd. All rights reserved.

KW - Averaging method

KW - Hopf bifurcation

KW - Michelson system

KW - Periodic orbit

U2 - https://doi.org/10.1016/j.nonrwa.2010.10.019

DO - https://doi.org/10.1016/j.nonrwa.2010.10.019

M3 - Article

VL - 12

SP - 1650

EP - 1653

JO - Nonlinear Analysis: Real World Applications

JF - Nonlinear Analysis: Real World Applications

SN - 1468-1218

ER -

On the Hopf-zero bifurcation of the Michelson system

Abstract

Keywords

Access to Document

Fingerprint

Cite this