Effective methods on determining the periodicity and form of solutions of some systems of non-linear difference equations

Various systems of non-linear difference equations, of different forms, were studied in the last two decades or so. In this existing work, two earlier published papers, due, respectively, to Bayram and Das. and Elsayed, 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 behaviour of solutions of a system of non-linear difference equations of higher order is investigated through analytical methods. The system, which is considered here, generalises those that are first presented in a paper of Elsayed 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 used to model real-life phenomena exhibiting periodic behaviours.