Phase Portraits of a Class of Cubic Systems with an Ellipse and a Straight Line as Invariant Algebraic Curves
Bakhshalizadeh, Ali (Isfahan University of Technology. Department of Mathematical Sciences)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2024
Abstract:	In this paper we classify the phase portraits in the Poincaré disc of a class of cubic polynomial differential systems having an invariant ellipse and an invariant straight line. We prove that such a class of cubic polynomial differential systems have exactly 43 topologically different phase portraits in the Poincaré disc. Also we obtain that the invariant ellipse in two of these phase portraits is a limit cycle.
Grants:	Agencia Estatal de Investigación PID2019-104658GB-I00 Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617 European Commission 777911
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Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Phase portraits in the Poincaré disc ; Limit cycle ; Cubic polynomial differential system ; Invariant ellipse ; Invariant straight line
Published in:	Differential Equations and Dynamical Systems, Vol. 32, Issue 3 (July 2024) , p. 871-907, ISSN 0974-6870

DOI: 10.1007/s12591-022-00597-9

Postprint 28 p, 1.1 MB

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