Acta Mathematica Sinica, English Series

, Volume 34, Issue 5, pp 801–811 | Cite as

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

  • Jaume Llibre
  • Claudia Valls


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.


Quadratic system complex ellipse invariant algebraic curves phase portrait Poincaré disc 

MR(2010) Subject Classification



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© 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 2017

Authors and Affiliations

  1. 1.Departament de MatemàtiquesUniversitat Autònoma de BarcelonaBellaterra, Barcelona, CataloniaSpain
  2. 2.Departamento de Matemática, Instituto Superior TécnicoUniversidade de LisboaLisboaPortugal

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