On the global flow of a 3-dimensional Lotka-Volterra system

Justino Alavez-Ramírez; Gamaliel Blé; Víctor Castellanos; Jaume Llibre

doi:https://doi.org/10.1016/j.na.2012.03.002

On the global flow of a 3-dimensional Lotka-Volterra system

Justino Alavez-Ramírez, Gamaliel Blé, Víctor Castellanos, Jaume Llibre

Department of Mathematics

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

9 Citations (Scopus)

Abstract

In the study of the black holes with a Higgs field appears in a natural way the Lotka-Volterra differential system ẋ=x(y-1),ẏ=y(1+y-2x 2-z 2),ż=zy, in ℝ 3. Here we provide the qualitative analysis of the flow of this system describing the α-limit set and the ω-limit set of all orbits of this system in the whole Poincaré ball, i.e. we identify ℝ 3 with the interior of the unit ball of ℝ 3 centered at the origin and we extend analytically this flow to its boundary, i.e. to the infinity. © 2012 Elsevier Ltd. All rights reserved.

Original language	English
Pages (from-to)	4114-4125
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	75
DOIs	https://doi.org/10.1016/j.na.2012.03.002
Publication status	Published - 1 Jun 2012

Keywords

Black hole
Higgs field
Lotka-Volterra system
Phase portrait
α-limit
ω-limit

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Cite this

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title = "On the global flow of a 3-dimensional Lotka-Volterra system",

abstract = "In the study of the black holes with a Higgs field appears in a natural way the Lotka-Volterra differential system ẋ=x(y-1),ẏ=y(1+y-2x 2-z 2),{\.z}=zy, in ℝ 3. Here we provide the qualitative analysis of the flow of this system describing the α-limit set and the ω-limit set of all orbits of this system in the whole Poincar{\'e} ball, i.e. we identify ℝ 3 with the interior of the unit ball of ℝ 3 centered at the origin and we extend analytically this flow to its boundary, i.e. to the infinity. {\textcopyright} 2012 Elsevier Ltd. All rights reserved.",

keywords = "Black hole, Higgs field, Lotka-Volterra system, Phase portrait, α-limit, ω-limit",

author = "Justino Alavez-Ram{\'i}rez and Gamaliel Bl{\'e} and V{\'i}ctor Castellanos and Jaume Llibre",

year = "2012",

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doi = "https://doi.org/10.1016/j.na.2012.03.002",

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TY - JOUR

T1 - On the global flow of a 3-dimensional Lotka-Volterra system

AU - Alavez-Ramírez, Justino

AU - Blé, Gamaliel

AU - Castellanos, Víctor

AU - Llibre, Jaume

PY - 2012/6/1

Y1 - 2012/6/1

N2 - In the study of the black holes with a Higgs field appears in a natural way the Lotka-Volterra differential system ẋ=x(y-1),ẏ=y(1+y-2x 2-z 2),ż=zy, in ℝ 3. Here we provide the qualitative analysis of the flow of this system describing the α-limit set and the ω-limit set of all orbits of this system in the whole Poincaré ball, i.e. we identify ℝ 3 with the interior of the unit ball of ℝ 3 centered at the origin and we extend analytically this flow to its boundary, i.e. to the infinity. © 2012 Elsevier Ltd. All rights reserved.

AB - In the study of the black holes with a Higgs field appears in a natural way the Lotka-Volterra differential system ẋ=x(y-1),ẏ=y(1+y-2x 2-z 2),ż=zy, in ℝ 3. Here we provide the qualitative analysis of the flow of this system describing the α-limit set and the ω-limit set of all orbits of this system in the whole Poincaré ball, i.e. we identify ℝ 3 with the interior of the unit ball of ℝ 3 centered at the origin and we extend analytically this flow to its boundary, i.e. to the infinity. © 2012 Elsevier Ltd. All rights reserved.

KW - Black hole

KW - Higgs field

KW - Lotka-Volterra system

KW - Phase portrait

KW - α-limit

KW - ω-limit

U2 - https://doi.org/10.1016/j.na.2012.03.002

DO - https://doi.org/10.1016/j.na.2012.03.002

M3 - Article

VL - 75

SP - 4114

EP - 4125

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

SN - 0362-546X

ER -

On the global flow of a 3-dimensional Lotka-Volterra system

Abstract

Keywords

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