Stability of the Planar Quadratic Systems from the Ring-Theoretic Viewpoint

Abstract

We show that the classical result on the stability of the origin in a quadratic planar system of ODEs can be formulated using either matrix theory or via its associated real and complex Marcus algebra. A generalization to a three-dimensional case is considered and some counterexamples provided.

Keywords

• quadratic differential systems
• commutative nonassociative algebra
• singular points
• stability