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

Jaume Llibre, Claudia Valls

Research output: Contribution to journalArticleResearchpeer-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 languageEnglish
Pages (from-to)801-811
JournalActa Mathematica Sinica, English Series
Volume34
Issue number5
DOIs
Publication statusPublished - 1 May 2018

Keywords

  • Poincaré disc
  • Quadratic system
  • complex ellipse
  • invariant algebraic curves
  • phase portrait

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