Glasnik matematički, Vol. 51 No. 1, 2016.
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
Publication date:
15.6.2016.
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