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′ = x − ay + bxz, z′ = cz − bxy. 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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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 -