Global phase portraits of quadratic differential systems exhibiting an invariant algebraic curve or an algebraic cubic first integral.

Abstract

Quadratic polynomial differential systems appear frequently in many areas of applied mathematics, electrical circuits, astrophysics, in population dynamics, chemistry, neural networks, laser physics, hydrodynamics, etc. Although these differential systems are the simplest nonlinear polynomial systems, they are also important as a basic testing ground for the general theory of the nonlinear differential systems.

Quadratic polynomial differential systems appear frequently in many areas of applied mathematics, electrical circuits, astrophysics, in population dynamics, chemistry, neural networks, laser physics, hydrodynamics, etc. Although these differential systems are the simplest nonlinear polynomial systems, they are also important as a basic testing ground for the general theory of the nonlinear differential systems.