Dynamical Behavior of Solution of Twenty-Fourth Order Rational Difference Equation

Abstract

This paper examines discrete-time systems, which are sometimes used to explain nonlinear natural phenomena in the sciences. Specifically, we investigate the boundedness, oscillation, stability, and exact solutions of nonlinear difference equations. We obtain these solutions using the standard iteration method and test the stability of equilibrium points using well-known theorems. We also provide numerical examples to validate our theoretical work and implement the numerical component using Wolfram Mathematica. The method presented can be easily applied to other rational recursive problems. \par

In this paper, we explore the dynamics of adhering to rational difference formula

\begin{equation*}

x_{n+1}=\frac{x_{n-23}}{\pm1\pm x_{n-5} x_{n-11}x_{n-17}x_{n-23}},

\end{equation*}

where the initials are arbitrary nonzero real numbers.