On the periodic orbit bifurcating from a zero Hopf bifurcation in systems with two slow and one fast variables

Isaac A. García; Jaume Llibre; Susanna Maza

doi:10.1016/j.amc.2013.12.184

On the periodic orbit bifurcating from a zero Hopf bifurcation in systems with two slow and one fast variables

Isaac A. García, Jaume Llibre, Susanna Maza

Departament de Matemàtiques

Producció científica: Contribució a revista › Article › Recerca › Avaluat per experts

15 Cites (Scopus)

Resum

The Hopf bifurcation in slow-fast systems with two slow variables and one fast variable has been studied recently, mainly from a numerical point of view. Our goal is to provide an analytic proof of the existence of the zero Hopf bifurcation exhibited for such systems, and to characterize the stability or instability of the periodic orbit which borns in such zero Hopf bifurcation. Our proofs use the averaging theory. © 2014 Elsevier Inc. All rights reserved.

Idioma original	Anglès
Pàgines (de-a)	84-90
Revista	Applied Mathematics and Computation
Volum	232
DOIs	https://doi.org/10.1016/j.amc.2013.12.184
Estat de la publicació	Publicada - 1 d’abr. 2014

Accés al document

10.1016/j.amc.2013.12.184

https://ddd.uab.cat/record/150743

Com citar-ho

@article{4c97bba06cd742c7af0ffffde52fc3a2,

title = "On the periodic orbit bifurcating from a zero Hopf bifurcation in systems with two slow and one fast variables",

abstract = "The Hopf bifurcation in slow-fast systems with two slow variables and one fast variable has been studied recently, mainly from a numerical point of view. Our goal is to provide an analytic proof of the existence of the zero Hopf bifurcation exhibited for such systems, and to characterize the stability or instability of the periodic orbit which borns in such zero Hopf bifurcation. Our proofs use the averaging theory. {\textcopyright} 2014 Elsevier Inc. All rights reserved.",

keywords = "Averaging theory, Singular perturbation, Zero Hopf bifurcation",

author = "Garc{\'i}a, {Isaac A.} and Jaume Llibre and Susanna Maza",

year = "2014",

month = apr,

day = "1",

doi = "10.1016/j.amc.2013.12.184",

language = "English",

volume = "232",

pages = "84--90",

journal = "Applied Mathematics and Computation",

issn = "0096-3003",

publisher = "Elsevier Inc.",

}

TY - JOUR

T1 - On the periodic orbit bifurcating from a zero Hopf bifurcation in systems with two slow and one fast variables

AU - García, Isaac A.

AU - Llibre, Jaume

AU - Maza, Susanna

PY - 2014/4/1

Y1 - 2014/4/1

N2 - The Hopf bifurcation in slow-fast systems with two slow variables and one fast variable has been studied recently, mainly from a numerical point of view. Our goal is to provide an analytic proof of the existence of the zero Hopf bifurcation exhibited for such systems, and to characterize the stability or instability of the periodic orbit which borns in such zero Hopf bifurcation. Our proofs use the averaging theory. © 2014 Elsevier Inc. All rights reserved.

AB - The Hopf bifurcation in slow-fast systems with two slow variables and one fast variable has been studied recently, mainly from a numerical point of view. Our goal is to provide an analytic proof of the existence of the zero Hopf bifurcation exhibited for such systems, and to characterize the stability or instability of the periodic orbit which borns in such zero Hopf bifurcation. Our proofs use the averaging theory. © 2014 Elsevier Inc. All rights reserved.

KW - Averaging theory

KW - Singular perturbation

KW - Zero Hopf bifurcation

U2 - 10.1016/j.amc.2013.12.184

DO - 10.1016/j.amc.2013.12.184

M3 - Article

SN - 0096-3003

VL - 232

SP - 84

EP - 90

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

ER -

On the periodic orbit bifurcating from a zero Hopf bifurcation in systems with two slow and one fast variables

Resum

Accés al document

Fingerprint

Com citar-ho