Journal of Nonlinear Mathematical Physics

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Volume 27, Issue 3, May 2020, Pages 509 - 519

Global dynamics of a Lotka–Volterra system in ℝ3

Authors
Jaume Llibre
Departament de Matemàtiques, Facultat de Ciències, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain,jllibre@mat.uab.cat
Y. Paulina Martínez
Centre de Recerca Matemática, 08193 Bellaterra, Barcelona, Catalonia, Spain,yohanna.martinez@uab.cat
Claudia Valls
Center for Mathematical Analysis, Geometry and Dynamical Systems, Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal,cvalls@math.tecnico.ulisboa.pt
Received 22 July 2019, Accepted 18 December 2019, Available Online 4 May 2020.
DOI
10.1080/14029251.2020.1757240How to use a DOI?
Keywords
Lotka–Volterra system; phase portraits; Poincaré ball
Abstract

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.

Copyright
© 2020 The Authors. Published by Atlantis and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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<Previous Article In Issue
Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
27 - 3
Pages
509 - 519
Publication Date
2020/05/04
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1080/14029251.2020.1757240How to use a DOI?
Copyright
© 2020 The Authors. Published by Atlantis and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

risenwbib
TY  - JOUR
AU  - Jaume Llibre
AU  - Y. Paulina Martínez
AU  - Claudia Valls
PY  - 2020
DA  - 2020/05/04
TI  - Global dynamics of a Lotka–Volterra system in ℝ³
JO  - Journal of Nonlinear Mathematical Physics
SP  - 509
EP  - 519
VL  - 27
IS  - 3
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2020.1757240
DO  - 10.1080/14029251.2020.1757240
ID  - Llibre2020
ER  -