Global phase portraits of the quadratic systems having a singular and irreducible invariant curve of degree 3
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Pantazi, Chara (Universitat Politècnica de Catalunya. Departament de Matemàtiques)

Date:	2023
Abstract:	Any singular irreducible cubic curve (or simply, cubic) after an affine transformation can be written as either y2 = x3, or y2 = x2(x + 1), or y2 = x2(x - 1). We classify the phase portraits of all quadratic polynomial differential systems having the invariant cubic y2 = x2(x + 1). We prove that there are 63 different topological phase portraits for such quadratic polynomial differential systems. We control all the bifurcations among these distinct topological phase portraits. These systems have no limit cycles. Only three phase portraits have a center, 19 of these phase portraits have one polycycle, three of these phase portraits have two polycycles. The maximum number of separartices that have these phase portraits is 26 and the minimum number is nine, the maximum number of canonical regions of these phase portraits is seven and the minimum is three.
Grants:	Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617 European Commission 777911 Agencia Estatal de Investigación MTM2016-77278-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1049 Agencia Estatal de Investigación PGC2018-098676-B-I00
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Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Poincaré disk ; Global phase portrait ; Singular curve ; Cubic curve ; Polycycles ; Canonical regions ; Separatrices
Published in:	International journal of bifurcation and chaos in applied sciences and engineering, Vol. 33, Issue 1 (January 2023) , art. 2350003, ISSN 1793-6551

DOI: 10.1142/S0218127423500037

Postprint 52 p, 2.1 MB

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Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
Articles > Published articles