2026-04-17T21:40:04Zhttps://recercat.cat/oai/request

oai:recercat.cat:2072/4862282025-08-31T18:30:18Zcom_2072_98col_2072_378192

Global dynamics analysis of a class of quadratic polynomial differential systems with an invariant plane in R3 Bakhshalizadeh, Ali Llibre, Jaume Rezende, Alex C. Differential systems in R3 Invariant plane Poincaré disc Poincaré ball Altres ajuts: Reial Acadèmia de Ciències i Arts de Barcelona 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. 2025 info:eu-repo/date/embargoEnd/2026-07-31 Article https://ddd.uab.cat/record/313599 urn:10.1007/s00030-025-01057-3 urn:oai:ddd.uab.cat:313599 urn:scopus_id:105007909974 urn:articleid:14209004v32n4p77 urn:gsduab:6034 urn:oai:egreta.uab.cat:publications/bd758a35-cf0e-4625-b93e-84731a777085 http://hdl.handle.net/2072/486228 eng Agencia Estatal de Investigación PID2022-136613NB-I00 Agència de Gestió d'Ajuts Universitaris i de Recerca 2021/SGR-00113 Nonlinear differential equations and applications ; Vol. 32, Issue 4 (July 2025), art. 77 embargoed access 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. https://rightsstatements.org/vocab/InC/1.0/