Global Phase Portraits of Quadratic Systems with a Complex Ellipse as Invariant Algebraic Curve

Authors
Llibre, Jaume Valls, Claudia
Citation
Llibre, Jaume et Valls, Claudia, Global Phase Portraits of Quadratic Systems with a Complex Ellipse as Invariant Algebraic Curve, Acta mathematica Sinica. English series (Print) , 34(5), 2018, pp. 801-811
Journal title
Acta mathematica Sinica. English series (Print) → ACNP
ISSN journal
14398516
Volume
34
Issue
5
Year of publication
2018
Pages
801 - 811
Database
ACNP
SICI code
Abstract
In this paper, we study a new class of quadratic systems and classify all its phase portraits. More precisely, we characterize the class of all quadratic polynomial differential systems in the plane having a complex ellipse x2 + y2 + 1 = 0 as invariant algebraic curve. We provide all the different topological phase portraits that this class exhibits in the Poincaré disc.