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

23 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

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

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AU - Zhang, Xiang

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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

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