Dynamical behavior of a system of third-order rational difference equation (Q1723371)

Summary: This paper deals with the boundedness, persistence, and global asymptotic stability of positive solution for a system of third-order rational difference equations \(x_{n + 1} = A + x_n / y_{n - 1} y_{n - 2}\), \(y_{n + 1} = A + y_n / x_{n - 1} x_{n - 2}\), \(n = 0,1, \ldots\), where \(A \in(0, \infty)\), \(x_{- i} \in(0, \infty)\); \(y_{- i} \in(0, \infty)\), \(i = 0,1, 2\). Some examples are given to demonstrate the effectiveness of the results obtained.