Original scientific paper

https://doi.org/10.3336/gm.51.1.10

Stability of critical points of quadratic homogeneous dynamical systems

Hamza Boujemaa orcid.org/0000-0001-8117-7227 ; Département de Mathématiques, Université Mohammed V-Rabat, 1014RP Rabat, Morocco
Said El Qotbi ; Systèmes Dynamiques, A3D, Université Mohammed V-Rabat, 1014RP Rabat, Morocco
Hicham Rouiouih ; Systèmes Dynamiques, A3D, Université Mohammed V-Rabat, 1014RP Rabat, Morocco

Abstract

In this work, we give sufficient conditions ensuring the instability of a critical point of a homogeneous quadratic system in Rn using the multiplication of the corresponding non-associative algebra. This result generalizes a theorem of Zalar and Mencinger (see [5]). We also state a classification theorem giving the stability or the instability of any stationary point of a quadratic homogeneous system in R2. As expected, the second theorem in [5] is part of this classification.

Keywords

Quadratic differential systems; non-associative algebra; critical points; stability; nilpotent

Hrčak ID:

160110

URI

https://hrcak.srce.hr/160110

Publication date:

15.6.2016.

Visits: 1.058 *