Stability Analysis of Critical Points in Quadratic Systems inR3Which Contain a Plane of Critical Points

Matej Mencinger
2003 Progress of Theoretical Physics Supplement  
Markus idea [ L. Markus, Quadratic Differential Equations and Nonassociative Algebras, Ann. Math. Studies 45 (Princeton Univ. Press, 1960), p. 185 ] of treating the quadratic systems of ODEs via commutative algebras which was introduced in 1960 is used in this paper to consider the stability of the origin. In [ M. Mencinger, submitted to Communications in Algebra ] all three-dimensional commutative algebras which contain a two-dimensional nil subalgebra were classified up to the algebraic
more » ... phism. This classification is used here to study the stability of the origin in the systems in Ê 3 with a plane of critical points.
doi:10.1143/ptps.150.388 fatcat:eck2t2ng2jdollr7qjpxm3esrq