many researches concerning the chaotic behavior have already been done.
They show that the simplest chaotic system must have at least 5 terms on the right
hand side of the ODE. In the present article we consider the homogeneous quadratic
systems which can be treated by algebraic tools. The family of homogeneous ODEs for
which the corresponding algebra contains a two-dimensional subalgebra is tested for
chaotic behavior. Using algebraic classification we show that there is no chaos in this family.
Key words: homogeneous, quadratic systems of ODEs, nonassociative algebra, nonchaotic behavior
