Glasnik Matematicki, Vol. 51, No. 1 (2016), 165-173.

STABILITY OF CRITICAL POINTS OF QUADRATIC HOMOGENEOUS DYNAMICAL SYSTEMS

Hamza Boujemaa, Said El Qotbi and Hicham Rouiouih

Département de Mathématiques, Université Mohammed V-Rabat, 1014RP Rabat, Morocco
e-mail: boujemaa@fsr.ac.ma

Systèmes Dynamiques, A3D, Université Mohammed V-Rabat, 1014RP Rabat, Morocco
e-mail: Qotbis@gmail.com

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.

2010 Mathematics Subject Classification.   34A34, 17A99.

Key words and phrases.   Quadratic differential systems, Non-associative algebra, critical points, Stability, Nilpotent.


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DOI: 10.3336/gm.51.1.10


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