Dynamics and Solutions of a Fifth-Order Nonlinear Difference Equation

Abstract

The main objective of this paper is to study the behavior of the rational difference equation of the fifth-order yn+1=αyn+βynyn-3/(Ayn-4+Byn-3), n=0,1,…, where α,β,A, and B are real numbers and the initial conditions y-4,y-3,y-2,y-1 and y0 are positive real numbers such that Ay-4+By-3≠0. Also, we obtain the solution of some special cases of this equation.