Journal of Nonlinear Mathematical Physics

Volume 27, Issue 3, May 2020, Pages 414 - 428

On the global dynamics of a three-dimensional forced-damped differential system

Authors
Jaume Llibre
Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain,jllibre@mat.uab.cat
Y. Paulina Martínez
Centre de Recerca Matemática, Campus Universitat Autònoma de Barcelona 08193 Bellaterra, Barcelona, Catalonia, Spain
Departamento de Matemática, Facultad de Ciencias, Universidad del Bío-Bío, Casilla 5-C, Concepción, Chile,yohanna.martinez@uab.cat;ymartinez@ubiobio.cl
Claudia Valls
Departamento de Matemática, Instituto Superior Técnico, Universidade Técnica de Lisboa, Av. Rovisco Pais 1049–001, Lisboa, Portugal,cvalls@math.ist.utl.pt
Received 30 April 2019, Accepted 14 October 2019, Available Online 4 May 2020.
DOI
10.1080/14029251.2020.1757232How to use a DOI?
Keywords
Global dynamics; Poincaré compactification; forced-damped system; invariant algebraic curve; invariant
Abstract

In this paper by using the Poincaré compactification of ℝ3 we make a global analysis of the model x′ = −ax + y + yz, y′ = xay + bxz, z′ = czbxy. In particular we give the complete description of its dynamics on the infinity sphere. For a + c = 0 or b = 1 this system has invariants. For these values of the parameters we provide the global phase portrait of the system in the Poincaré ball. We also describe the α and ω-limit sets of its orbits in the Poincaré ball.

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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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
27 - 3
Pages
414 - 428
Publication Date
2020/05/04
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1080/14029251.2020.1757232How 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

TY  - JOUR
AU  - Jaume Llibre
AU  - Y. Paulina Martínez
AU  - Claudia Valls
PY  - 2020
DA  - 2020/05/04
TI  - On the global dynamics of a three-dimensional forced-damped differential system
JO  - Journal of Nonlinear Mathematical Physics
SP  - 414
EP  - 428
VL  - 27
IS  - 3
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2020.1757232
DO  - 10.1080/14029251.2020.1757232
ID  - Llibre2020
ER  -