Solution of the rational difference equation xn+1=xn-17/1+xn-5•xn-11

Abstract

In this paper, solution of the following difference equation is examined x n+1 = x n−17 1 + x n−5 .x n−11 , where the initial conditions are positive reel numbers.

Analytical Study of Nonlinear Systems of Higher-Order Difference Equations: Solutions, Stability, and Numerical Simulations

“…Our work provides a deeper analysis of the behavior of bidimensional systems, while Abo-Zeid's [17] work revolves around studying the details of explicit solutions and the general behavior of specific models. The study by Simşek et al [18] focuses on solving a specific rational difference equation, with a particular focus on providing explicit solutions and analyzing the behavior of the solutions. In contrast, our paper delves into the examination of a broader range of rational difference equations, exploring various forms and complexities.…”