Journal of Nonlinear Mathematical Physics

Volume 24, Issue 4, September 2017, Pages 473 - 494

On the Darboux integrability 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
Regilene Oliveira
Departamento de Matemática, ICMC, Universidade de São Paulo, Av. Trabalhador São-carlense, 400, 13566-590, São Carlos, SP, Brazil.regilene@icmc.usp.br
Claudia Valls
Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais 1049-001, Lisboa, Portugal.cvalls@math.ist.utl.pt
Received 10 September 2016, Accepted 23 May 2017, Available Online 6 January 2021.
DOI
10.1080/14029251.2017.1375686How to use a DOI?
Keywords
Invariant algebraic surfaces; exponential factors; first integral; four-scroll chaotic system
Abstract

In 2011 Pehlivan proposed a three–dimensional forced–damped autonomous differential system which can display simultaneously unbounded and chaotic solutions. This untypical phenomenon has been studied recently by several authors. In this paper we study the opposite to its chaotic motion, i.e. its integrability, mainly the existence of polynomial, rational and Darboux first integrals through the analysis of its invariant algebraic surfaces and its exponential factors.

Copyright
© 2017 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC license.

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
24 - 4
Pages
473 - 494
Publication Date
2021/01/06
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1080/14029251.2017.1375686How to use a DOI?
Copyright
© 2017 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - JOUR
AU  - Jaume Llibre
AU  - Regilene Oliveira
AU  - Claudia Valls
PY  - 2021
DA  - 2021/01/06
TI  - On the Darboux integrability of a three–dimensional forced–damped differential system
JO  - Journal of Nonlinear Mathematical Physics
SP  - 473
EP  - 494
VL  - 24
IS  - 4
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2017.1375686
DO  - 10.1080/14029251.2017.1375686
ID  - Llibre2021
ER  -