Effective Methods on Determining the Periodicity and Form of Solutions of Some Systems of Nonlinear Difference Equations

Julius Fergy T. Rabago

Published 2015-12-05Version 1

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.