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

TL;DR

This paper revisits and extends previous studies on nonlinear difference equations, offering a more theoretical approach to analyze the periodicity and solutions of higher-order systems with potential applications in modeling real-world phenomena.

Contribution

It introduces a new theoretical method for analyzing the periodicity and solutions of nonlinear difference systems, generalizing earlier models and providing deeper qualitative insights.

Findings

Re-examination of previous results with a new approach

Analysis of higher-order nonlinear difference systems

Potential applications in modeling periodic real-life phenomena

Abstract

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.