On Dynamics of A Higher-Order Rational Difference Equation

Abstract

In this paper, we study the dynamical behavior of the positive solutions of the difference equation $ y_{n+1}=\frac{A+By_{n}}{C+D\prod_{i=1}^{k}y_{n-i}^{q_{i}}},\ n\in \mathbb{N}_{0} $ where $\mathbb{N}_{0}=\mathbb{N} \cup \left\{ 0\right\} $, the initial conditions and the parameters $A,$ $B$ are non-negative real numbers, the parameters $C$, $D$\ are positive real numbers, $q_{i}$ for $i\in \{1,2,...k\}$ are fixed positive integers and $% 1\leq k$.