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

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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.

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Authors and Affiliations

  1. Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193, Bellaterra, Barcelona, Catalonia, Spain

    Jaume Llibre

  2. Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, 1049–001, Lisboa, Portugal

    Claudia Valls

Authors
  1. Jaume Llibre
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  2. Claudia Valls
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Corresponding author

Correspondence to Jaume Llibre.

Additional information

The first author is partially supported by a MINECO/FEDER grant MTM2013-40998-P, an AGAUR grant number 2014 SGR568, the grants FP7-PEOPLE-2012-IRSES 318999 and 316338, and the MINECO/FEDER grant UNAB13-4E-1604. The second author is partially supported by FCT/Portugal through UID/MAT/04459/2013

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Llibre, J., Valls, C. Global Phase Portraits of Quadratic Systems with a Complex Ellipse as Invariant Algebraic Curve. Acta. Math. Sin.-English Ser. 34, 801–811 (2018). https://doi.org/10.1007/s10114-017-5478-y

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

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