Zero-Hopf bifurcation in the generalized Michelson system

Jaume Llibre; Amar Makhlouf

doi:https://doi.org/10.1016/j.chaos.2015.11.013

Zero-Hopf bifurcation in the generalized Michelson system

Jaume Llibre, Amar Makhlouf

Department of Mathematics

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

17 Citations (Scopus)

Abstract

© 2015 Elsevier Ltd We provide sufficient conditions for the existence of two periodic solutions bifurcating from a zero–Hopf equilibrium for the differential systemx˙=y,y˙=z,z˙=a+by+cz−x2/2,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.

Original language	English
Pages (from-to)	228-231
Journal	Chaos, Solitons and Fractals
Volume	89
DOIs	https://doi.org/10.1016/j.chaos.2015.11.013
Publication status	Published - 1 Aug 2016

Keywords

Averaging theory
Michelson system
Periodic solution
Triple-zero bifurcation
Zero–Hopf Bifurcation

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https://doi.org/10.1016/j.chaos.2015.11.013

https://ddd.uab.cat/record/169445

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title = "Zero-Hopf bifurcation in the generalized Michelson system",

abstract = "{\textcopyright} 2015 Elsevier Ltd We provide sufficient conditions for the existence of two periodic solutions bifurcating from a zero–Hopf equilibrium for the differential systemx˙=y,y˙=z,z˙=a+by+cz−x2/2,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.",

keywords = "Averaging theory, Michelson system, Periodic solution, Triple-zero bifurcation, Zero–Hopf Bifurcation",

author = "Jaume Llibre and Amar Makhlouf",

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T1 - Zero-Hopf bifurcation in the generalized Michelson system

AU - Llibre, Jaume

AU - Makhlouf, Amar

PY - 2016/8/1

Y1 - 2016/8/1

N2 - © 2015 Elsevier Ltd We provide sufficient conditions for the existence of two periodic solutions bifurcating from a zero–Hopf equilibrium for the differential systemx˙=y,y˙=z,z˙=a+by+cz−x2/2,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.

AB - © 2015 Elsevier Ltd We provide sufficient conditions for the existence of two periodic solutions bifurcating from a zero–Hopf equilibrium for the differential systemx˙=y,y˙=z,z˙=a+by+cz−x2/2,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.

KW - Averaging theory

KW - Michelson system

KW - Periodic solution

KW - Triple-zero bifurcation

KW - Zero–Hopf Bifurcation

U2 - https://doi.org/10.1016/j.chaos.2015.11.013

DO - https://doi.org/10.1016/j.chaos.2015.11.013

M3 - Article

SN - 0960-0779

VL - 89

SP - 228

EP - 231

JO - Chaos, Solitons and Fractals

JF - Chaos, Solitons and Fractals

ER -

Zero-Hopf bifurcation in the generalized Michelson system

Abstract

Keywords

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