Electron. J. Differential Equations, Vol. 2018 (2018), No. 141, pp. 1-19.

Global phase portraits for quadratic systems with a hyperbola and a straight line as invariant algebraic curves

Jaume Llibre, Jiang Yu

In this article we consider a class of quadratic polynomial differential systems in the plane having a hyperbola and a straight line as invariant algebraic curves, and we classify all its phase portraits. Moreover these systems are integrable and we provide their first integrals.

Submitted May 25, 2016. Published July 11, 2018.
Math Subject Classifications: 34C05.
Key Words: Quadratic system, first integral, global phase portraits, invariant hperbola, invariant straight line.

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Jaume Llibre
Departament de Matemàtiques
Universitat Autònoma 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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