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

Abstract

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.

Keywords

• Quadratic system, first integral, global phase portraits,
• invariant hperbola, invariant straight line