Dynamical Analysis and Solutions of Nonlinear Difference Equations of Thirty Order

Abstract

Discrete-time systems are sometimes used to explain natural phenomena that happen in nonlinear sciences. We study the periodicity, boundedness, oscillation, stability, and certain exact solutions of nonlinear difference equations in this paper. Using the standard iteration method, exact solutions are obtained. Some well-known theorems are used to test the stability of the equilibrium points. Some numerical examples are also provided to confirm the theoretical work’s validity. The numerical component is implemented with Wolfram Mathematica. The method presented may be simply applied to other rational recursive issues. \par In this paper, we explore the dynamics of adhering to rational difference formula \begin{equation*} x_{n+1}=\frac{x_{n-29}}{\pm1\pm x_{n-5}x_{n-11}x_{n-17}x_{n-23}x_{n-29}}, \end{equation*} where the initials are arbitrary nonzero real numbers.