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 |
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Pages (from-to) | 801-811 |
Journal | Acta Mathematica Sinica, English Series |
Volume | 34 |
Issue number | 5 |
DOIs | |
Publication status | Published - 1 May 2018 |
Keywords
- Poincaré disc
- Quadratic system
- complex ellipse
- invariant algebraic curves
- phase portrait