On Dynamics and Solutions Expressions of Higher-Order Rational Difference Equations

Abstract

The principle goal of this paper is to look at some of the qualitative behavior of the critical point of the rational difference equation
 
 Ψ_{n+1}=αΨ_{n-2}+((βΨ_{n-2}Ψ_{n-3})/(γΨ_{n-3}+δΨ_{n-6})), n=0,1,2,...,
 
 where α,β,γ and δ are arbitrary positive real numbers. We also used the proposed equation to get the general solution for particular cases and provided numerical examples to demonstrate our results.

Dynamics and general form of the solutions of rational difference equations

“…Elsayed and Al-Rakhami investigated the qualitative behavior of the critical point and found the solution for a rational recursive sequence in [19]…”