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

Jaume Llibre; Claudia Valls

doi:https://doi.org/10.1007/s10114-017-5478-y

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

Jaume Llibre, Claudia Valls

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

Abstract

© 2017, Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature. 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.

Original language	English
Pages (from-to)	801-811
Journal	Acta Mathematica Sinica, English Series
Volume	34
Issue number	5
DOIs	https://doi.org/10.1007/s10114-017-5478-y
Publication status	Published - 1 May 2018

Keywords

Poincaré disc
Quadratic system
complex ellipse
invariant algebraic curves
phase portrait

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