Abstract
© 2015 Texas State University. In this article we study a class of integrable quadratic systems and classify all its phase portraits. More precisely, we characterize the class of all quadratic polynomial differential systems in the plane having an ellipse and a straight line as invariant algebraic curves. We show that this class is integrable and we provide all the different topological phase portraits that this class exhibits in the Poincaré disc.
Original language | English |
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Journal | Electronic Journal of Differential Equations |
Volume | 2015 |
Publication status | Published - 24 Dec 2015 |
Keywords
- First integral
- Global phase portraits
- Invariant ellipse
- Invariant straight line
- Quadratic system