Hopf bifurcation in 3-dimensional polynomial vector fields

Iván Sánchez-Sánchez; Joan Torregrosa

doi:10.1016/j.cnsns.2021.106068

Hopf bifurcation in 3-dimensional polynomial vector fields

Iván Sánchez-Sánchez, Joan Torregrosa

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In this work we study the local cyclicity of some polynomial vector fields in R ³. In particular, we give a quadratic system with 11 limit cycles, a cubic system with 31 limit cycles, a quartic system with 54 limit cycles, and a quintic system with 92 limit cycles. All limit cycles are small amplitude limit cycles and bifurcate from a Hopf type equilibrium. We introduce how to find Lyapunov constants in R ³ for considering the usual degenerate Hopf bifurcation with a parallelization approach, which enables to prove our results for 4th and 5th degrees.

Idioma original	English
Nombre de pàgines	13
Revista	Communications in Nonlinear Science and Numerical Simulation
Volum	105
DOIs	https://doi.org/10.1016/j.cnsns.2021.106068
Estat de la publicació	Publicada - 1 de febr. 2022

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10.1016/j.cnsns.2021.106068

https://ddd.uab.cat/record/258889

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title = "Hopf bifurcation in 3-dimensional polynomial vector fields",

abstract = "In this work we study the local cyclicity of some polynomial vector fields in R 3. In particular, we give a quadratic system with 11 limit cycles, a cubic system with 31 limit cycles, a quartic system with 54 limit cycles, and a quintic system with 92 limit cycles. All limit cycles are small amplitude limit cycles and bifurcate from a Hopf type equilibrium. We introduce how to find Lyapunov constants in R 3 for considering the usual degenerate Hopf bifurcation with a parallelization approach, which enables to prove our results for 4th and 5th degrees. ",

keywords = "Hopf bifurcation in dimension three, Limit cycles, Lyapunov constants",

author = "Iv{\'a}n S{\'a}nchez-S{\'a}nchez and Joan Torregrosa",

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year = "2022",

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doi = "10.1016/j.cnsns.2021.106068",

language = "English",

volume = "105",

journal = "Communications in Nonlinear Science and Numerical Simulation",

issn = "1007-5704",

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TY - JOUR

T1 - Hopf bifurcation in 3-dimensional polynomial vector fields

AU - Sánchez-Sánchez, Iván

AU - Torregrosa, Joan

N1 - DBLP License: DBLP's bibliographic metadata records provided through http://dblp.org/ are distributed under a Creative Commons CC0 1.0 Universal Public Domain Dedication. Although the bibliographic metadata records are provided consistent with CC0 1.0 Dedication, the content described by the metadata records is not. Content may be subject to copyright, rights of privacy, rights of publicity and other restrictions.

PY - 2022/2/1

Y1 - 2022/2/1

N2 - In this work we study the local cyclicity of some polynomial vector fields in R 3. In particular, we give a quadratic system with 11 limit cycles, a cubic system with 31 limit cycles, a quartic system with 54 limit cycles, and a quintic system with 92 limit cycles. All limit cycles are small amplitude limit cycles and bifurcate from a Hopf type equilibrium. We introduce how to find Lyapunov constants in R 3 for considering the usual degenerate Hopf bifurcation with a parallelization approach, which enables to prove our results for 4th and 5th degrees.

AB - In this work we study the local cyclicity of some polynomial vector fields in R 3. In particular, we give a quadratic system with 11 limit cycles, a cubic system with 31 limit cycles, a quartic system with 54 limit cycles, and a quintic system with 92 limit cycles. All limit cycles are small amplitude limit cycles and bifurcate from a Hopf type equilibrium. We introduce how to find Lyapunov constants in R 3 for considering the usual degenerate Hopf bifurcation with a parallelization approach, which enables to prove our results for 4th and 5th degrees.

KW - Hopf bifurcation in dimension three

KW - Limit cycles

KW - Lyapunov constants

UR - https://doi.org/10.1016/j.cnsns.2021.106068

UR - http://www.scopus.com/inward/record.url?scp=85118484165&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/09189a67-90a6-3838-9e31-d6066aa547f6/

U2 - 10.1016/j.cnsns.2021.106068

DO - 10.1016/j.cnsns.2021.106068

M3 - Article

SN - 1007-5704

VL - 105

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

ER -

Hopf bifurcation in 3-dimensional polynomial vector fields

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