Dynamical Behavior of a System of Third-Order Rational Difference Equation

Abstract

This paper deals with the boundedness, persistence, and global asymptotic stability of positive solution for a system of third-order rational difference equations xn+1=A+xn/yn-1yn-2, yn+1=A+yn/xn-1xn-2, n=0,1,…, where A∈(0,∞), x-i∈(0,∞); y-i∈(0,∞), i=0,1,2. Some examples are given to demonstrate the effectiveness of the results obtained.