Electron. J. Diff. Equ., Vol. 2015 (2015), No. 314, pp. 1-14.

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

Jaume Llibre, Jiang Yu

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.

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Jaume Llibre
Departament de Matemátiques
Universitat Autónoma de Barcelona
08193 Bellaterra, Barcelona, Catalonia, Spain
email: jllibre@mat.uab.cat
Jiang Yu
Department of Mathematics
Shanghai Jiao Tong University
Shanghai 200240, China
email: jiangyu@sjtu.edu.cn

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