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.