Electronic Journal of Differential Equations,
Vol. 2015 (2015), No. 314, pp. 1-14.

Title: Global phase portraits of quadratic systems with an ellipse and a
       straight line as invariant algebraic curves

Authors: Jaume Llibre (Univ. Autonoma de Barcelona, Catalonia, Spain)
         Jiang Yu (Shanghai Jiao Tong Univ., Shanghai, China)


Abstract: 
 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 Poincare disc.

Submitted September 4, 2015. Published December 24, 2015.
Math Subject Classifications: 34C05.
Key Words: Quadratic system; first integral; global phase portraits;
           invariant ellipse; invariant straight line.