Dynamical Behavior of Solution of Fifteenth-Order Rational Difference Equation

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 of generalized order 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 confirmthe theoretical work’s validity. The numerical component is implemented withWolfram Mathematica. The method presented may be simply applied to other rational recursive issues.
In this research, we examine the qualitative behavior of rational recursive sequences provided that the initial conditions are arbitrary real numbers. We examine the behavior of solutions on graphs according to the state of their initial value
xn+1 = xn−2xn−8xn−14
±xn−5xn−11 ± xn−2xn−5xn−8xn−11xn−14
.