Solutions and Solution Behavior of Difference Equation Systems

Abstract

 The behaviour of the solutions of the following system of difference equations is examined. In this study, the solutions of the initial conditions in the range (0,1) and the behavior of the solutions were examined. Investigations on the recent studies show that researches nature of nonlinear difference equations have been an object of great interest. Although difference equations are relatively simple in form, it is, unfortunately, extremely difficult to understand thoroughly the periodic and non periodic behavior of their solutions. Nonlinear difference equations of the max type has been investigated by many authors. These equations are particularly utilized in various fields, including population dynamics, economics, finance, and control systems. Max-type difference equations are not only interesting from a theoretical perspective but also possess a wide range of practical applications. They are frequently employed to model discrete dynamical systems in control theory, economic fluctuations, and biological population models with delayed feedback mechanisms. Understanding the periodic behavior and stability of such systems provides vital insights into the long-term dynamics of these real-world phenomena. In addition, Mathematica software was employed to generate the graphical illustrations and numerical examples presented in this study.