Global Phase Portraits of Quadratic Systems with a Complex Ellipse as Invariant Algebraic Curve
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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.
KeywordsQuadratic system complex ellipse invariant algebraic curves phase portrait Poincaré disc
MR(2010) Subject Classification34C05
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