摘要：Closed form formulas of the solutions to the following system of difference equations: x n = y n − 1 y n − 2 x n − 1 ( a n + b n y n − 1 y n − 2 ) , y n = x n − 1 x n − 2 y n − 1 ( α n + β n x n − 1 x n − 2 ) , n ∈ N 0 , $$x_{n}=\frac{y_{n-1}y_{n-2}}{x_{n-1}(a_{n}+b_{n}y_{n-1}y_{n-2})},\qquad y_{n}=\frac{x_{n-1}x_{n-2}}{y_{n-1}(\alpha _{n}+\beta _{n}x_{n-1}x_{n-2})},\quad n\in \mathbb {N}_(, $$ where a n $a_{n}$ , b n $b_{n}$ , α n $\alpha _{n}$ , β n $\beta _{n}$ , n ∈ N 0 $n\in \mathbb {N}_($ , and initial values x − i $x_{-i}$ , y − i $y_{-i}$ , i ∈ { 1 , 2 } $i\in\{1,2\}$ are real numbers, are found. The domain of undefinable solutions to the system is described. The long-term behavior of its solutions is studied in detail for the case of constant a n $a_{n}$ , b n $b_{n}$ , α n $\alpha _{n}$ and β n $\beta _{n}$ , n ∈ N 0 $n\in \mathbb {N}_($ .
关键词：system of difference equations ; closed form solution ; long-term behavior ; periodic solutions
