Phase Portraits of the Equation x¨ + axx˙ + bx3 = 0
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática)

Date:	2024
Abstract:	The second-order differential equation x¨ + axx˙ + bx3 = 0 with a, b ∈ R has been studied by several authors mainly due to its applications. Here, for the first time, we classify all its phase portraits in function of its parameters a and b. This classification is done in the Poincaré disc in order to control the orbits which scape or come from infinity. We prove that there are exactly six topologically different phase portraits in the Poincar'e disc of the first order differential system associated by the second-order differential equation. Additionally we show that this system is always integrable providing explicitly its first integrals.
Grants:	Agencia Estatal de Investigación PID2022-136613NB-I00 European Commission 777911 Agència de Gestió d'Ajuts Universitaris i de Recerca 2021/SGR-00113
Note:	Altres ajuts: Reial Acadèmia de Ciències i Arts de Barcelona
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Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Second-order differential equation ; Poincaré compactification ; Global phase portraits
Published in:	Regular and Chaotic Dynamics, Vol. 29, Issue 6 (December 2024) , p. 825-837, ISSN 1468-4845

DOI: 10.1134/S1560354724560053

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Articles > Research articles
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