Three-Dimensional Lotka–Volterra Systems with 3:−1:2-Resonance

Waleed Aziz; Colin Christopher; Jaume Llibre; Chara Pantazi

doi:10.1007/s00009-021-01809-2

Three-Dimensional Lotka–Volterra Systems with 3:−1:2-Resonance

Waleed Aziz, Colin Christopher, Jaume Llibre, Chara Pantazi^*

^*Autor corresponent d’aquest treball

Departament de Matemàtiques

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Resum

We study the local integrability at the origin of a nine-parameter family of three-dimensional Lotka–Volterra differential systems with (3:− 1:2)-resonance. We give necessary and sufficient conditions on the parameters of the family that guarantee the existence of two independent local first integrals at the origin of coordinates. Additionally, we classify those cases where the origin is linearizable.

Idioma original	Anglès
Número d’article	167
Nombre de pàgines	24
Revista	Mediterranean Journal of Mathematics
Volum	18
Número	4
DOIs	https://doi.org/10.1007/s00009-021-01809-2
Estat de la publicació	Publicada - d’ag. 2021

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10.1007/s00009-021-01809-2

https://ddd.uab.cat/record/257098

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title = "Three-Dimensional Lotka–Volterra Systems with 3:−1:2-Resonance",

abstract = "We study the local integrability at the origin of a nine-parameter family of three-dimensional Lotka–Volterra differential systems with (3:− 1:2)-resonance. We give necessary and sufficient conditions on the parameters of the family that guarantee the existence of two independent local first integrals at the origin of coordinates. Additionally, we classify those cases where the origin is linearizable.",

keywords = "Jacobi multiplier, Lotka–Volterra, integrability, linearizability",

author = "Waleed Aziz and Colin Christopher and Jaume Llibre and Chara Pantazi",

note = "Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.",

year = "2021",

month = aug,

doi = "10.1007/s00009-021-01809-2",

language = "English",

volume = "18",

journal = "Mediterranean Journal of Mathematics",

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TY - JOUR

T1 - Three-Dimensional Lotka–Volterra Systems with 3:−1:2-Resonance

AU - Aziz, Waleed

AU - Christopher, Colin

AU - Llibre, Jaume

AU - Pantazi, Chara

PY - 2021/8

Y1 - 2021/8

N2 - We study the local integrability at the origin of a nine-parameter family of three-dimensional Lotka–Volterra differential systems with (3:− 1:2)-resonance. We give necessary and sufficient conditions on the parameters of the family that guarantee the existence of two independent local first integrals at the origin of coordinates. Additionally, we classify those cases where the origin is linearizable.

AB - We study the local integrability at the origin of a nine-parameter family of three-dimensional Lotka–Volterra differential systems with (3:− 1:2)-resonance. We give necessary and sufficient conditions on the parameters of the family that guarantee the existence of two independent local first integrals at the origin of coordinates. Additionally, we classify those cases where the origin is linearizable.

KW - Jacobi multiplier

KW - Lotka–Volterra

KW - integrability

KW - linearizability

UR - https://www.scopus.com/pages/publications/85107652695

U2 - 10.1007/s00009-021-01809-2

DO - 10.1007/s00009-021-01809-2

M3 - Article

AN - SCOPUS:85107652695

SN - 1660-5446

VL - 18

JO - Mediterranean Journal of Mathematics

JF - Mediterranean Journal of Mathematics

IS - 4

M1 - 167

ER -

Three-Dimensional Lotka–Volterra Systems with 3:−1:2-Resonance

Resum

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