Global dynamics analysis of a class of quadratic polynomial differential systems with an invariant plane in R3
Bakhshalizadeh, Ali (Universidade Federal de São Carlos. Departamento de Matemática)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Rezende, Alex C. (Universidade Federal de São Carlos. Departamento de Matemática)

Date:	2025
Abstract:	In this paper we study a class of quadratic differential systems in R3. More precisely, for three distinct families of parameter sets, such differential systems exhibit the property of having an invariant plane. The first family exhibits a first integral in the form of H(x, y) = ax + by ensures the invariance of every plane ax + by = constant. Consequently, we describe the phase portraits of the system on each of such planes in the Poincaré disc. The second family has a Darboux invariant of the form I(x, y, t) = d0 + d1x + d2ye-k0t which will allow us to describe the phase portraits on the Poincaré ball. Unlike the first two families, the third family lacks both a first integral and a Darboux invariant. Nevertheless, we present a detailed analysis of the phase portraits of these systems on the invariant plane using the Poincaré disc.
Grants:	Agencia Estatal de Investigación PID2022-136613NB-I00 Agència de Gestió d'Ajuts Universitaris i de Recerca 2021/SGR-00113
Note:	Altres ajuts: Reial Acadèmia de Ciències i Arts de Barcelona
Rights:	Aquest material està protegit per drets d'autor i/o drets afins. Podeu utilitzar aquest material en funció del que permet la legislació de drets d'autor i drets afins d'aplicació al vostre cas. Per a d'altres usos heu d'obtenir permís del(s) titular(s) de drets.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Differential systems in R3 ; Invariant plane ; Poincaré disc ; Poincaré ball
Published in:	Nonlinear differential equations and applications, Vol. 32, Issue 4 (July 2025) , art. 77, ISSN 1420-9004

DOI: 10.1007/s00030-025-01057-3

Available from: 2026-07-31 Postprint

The record appears in these collections:
Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
Articles > Published articles