  Recently, various systems of nonlinear difference equations, of different
forms, were studied. In this existing work, two earlier published papers, due
respectively to Bayram and Das. [Appl. Math. Sci. (Ruse), 4(7) (2010) pp.
817-821] and Elsayed [Fasciculi Mathematici, 40 (2008), pp. 5-13], are
revisited. The results exhibited in these previous investigations are
re-examined through a new approach, more theoretical and explanative compared
to the ones offered in these aforementioned works. Furthermore, the qualitative
behavior of solutions of a system of nonlinear difference equations of
higher-order is investigated through analytical methods. The system, which is
considered here, generalizes those that are first presented in [Fasciculi
Mathematici, 40 (2008), pp. 5-13] but are treated differently from this
pre-existing work. The results delivered here are important, not only for the
reason that they provide theoretical explanations on several earlier results,
but also because the system being studied can be use to model real-life
phenomena exhibiting periodic behaviors.
