© 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.
|Journal||Electronic Journal of Differential Equations|
|Publication status||Published - 24 Dec 2015|
- First integral
- Global phase portraits
- Invariant ellipse
- Invariant straight line
- Quadratic system