Global dynamics of a Lotka-Volterra system in R³

In this work we consider the Lotka-Volterra system in R³ x˙ = -x(x - y - z), y˙ = -y(-x + y - z), z˙ = -z(-x - y + z), introduced recently in [7], and studied also in [8] and [14]. In the first two papers the authors mainly studied the integrability of this differential system, while in the third pa...

Descripción completa

Detalles Bibliográficos
Autores: Llibre, Jaume|||0000-0002-9511-5999, Martínez, Y. Paulina|||0000-0003-1430-6636, Valls, Clàudia|||0000-0001-8279-1229
Tipo de recurso: artículo
Fecha de publicación:2020
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:228109
Acceso en línea:https://ddd.uab.cat/record/228109
https://dx.doi.org/urn:doi:10.1080/14029251.2020.1757240
Access Level:acceso abierto
Palabra clave:Lotka-Volterra system
Phase portraits
Poincaré ball
Descripción
Sumario:In this work we consider the Lotka-Volterra system in R³ x˙ = -x(x - y - z), y˙ = -y(-x + y - z), z˙ = -z(-x - y + z), introduced recently in [7], and studied also in [8] and [14]. In the first two papers the authors mainly studied the integrability of this differential system, while in the third paper they studied the system as a Hamilton-Poisson system, and also started the analysis of its dynamics. Here we provide the global phase portraits of this 3-dimensional Lotka-Volterra system in the Poincaré ball, that is in R³ adding its extension to the infinity.