Mathematics (May 2022)

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

  • Borut Zalar,
  • Matej Mencinger

DOI
https://doi.org/10.3390/math10101629
Journal volume & issue
Vol. 10, no. 10
p. 1629

Abstract

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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.

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