Dynamics of a family of Lotka–Volterra systems in R3

Jaume Llibre; Y. Paulina Martínez

doi:10.1016/j.na.2020.111915

Dynamics of a family of Lotka–Volterra systems in R³

Jaume Llibre, Y. Paulina Martínez^*

^*Autor corresponent d’aquest treball

Departament de Matemàtiques

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8 Cites (Scopus)

Resum

We provide the phase portraits of the 3-dimensional Lotka–Volterra systems ẋ=x(y+az),ẏ=y(x+z),ż=bz(−ax+y), for all the values of the parameters a and b, in the finite region and in the infinity region through the Poincaré compactification. We also study the integrability of the system.

Idioma original	Anglès
Número d’article	111915
Revista	Nonlinear Analysis, Theory, Methods and Applications
Volum	199
DOIs	https://doi.org/10.1016/j.na.2020.111915
Estat de la publicació	Publicada - d’oct. 2020

Accés al document

10.1016/j.na.2020.111915

https://ddd.uab.cat/record/228120

Altres arxius i enllaços

Link to publication in Scopus

Com citar-ho

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title = "Dynamics of a family of Lotka–Volterra systems in R3",

abstract = "We provide the phase portraits of the 3-dimensional Lotka–Volterra systems ẋ=x(y+az),ẏ=y(x+z),{\.z}=bz(−ax+y), for all the values of the parameters a and b, in the finite region and in the infinity region through the Poincar{\'e} compactification. We also study the integrability of the system.",

keywords = "Integrability, Lotka–Volterra, Phase portraits, Poincar{\'e} disc",

author = "Jaume Llibre and Mart{\'i}nez, \{Y. Paulina\}",

note = "Publisher Copyright: {\textcopyright} 2020 Elsevier Ltd",

year = "2020",

month = oct,

doi = "10.1016/j.na.2020.111915",

language = "English",

volume = "199",

journal = "Nonlinear Analysis, Theory, Methods and Applications",

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TY - JOUR

T1 - Dynamics of a family of Lotka–Volterra systems in R3

AU - Llibre, Jaume

AU - Martínez, Y. Paulina

PY - 2020/10

Y1 - 2020/10

N2 - We provide the phase portraits of the 3-dimensional Lotka–Volterra systems ẋ=x(y+az),ẏ=y(x+z),ż=bz(−ax+y), for all the values of the parameters a and b, in the finite region and in the infinity region through the Poincaré compactification. We also study the integrability of the system.

AB - We provide the phase portraits of the 3-dimensional Lotka–Volterra systems ẋ=x(y+az),ẏ=y(x+z),ż=bz(−ax+y), for all the values of the parameters a and b, in the finite region and in the infinity region through the Poincaré compactification. We also study the integrability of the system.

KW - Integrability

KW - Lotka–Volterra

KW - Phase portraits

KW - Poincaré disc

UR - https://www.scopus.com/pages/publications/85084188178

U2 - 10.1016/j.na.2020.111915

DO - 10.1016/j.na.2020.111915

M3 - Article

AN - SCOPUS:85084188178

SN - 0362-546X

VL - 199

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

M1 - 111915