Behavior and periodic solutions of a two-dimensional systems of rational difference equations

This paper is devoted to investigate the local asymptotic stability, boundedness and periodic solutions of particular cases of the following general system of difference equations: x_{n+1}=\frac{a_{1}y_{n-1}+a_{2}x_{n-3}+a_{3}}{a_{4}y_{n-1}x_{n-3}+a_{5}},\text{ \ \ \ \ }y_{n+1}=\frac{b_{1}x_{n-1}+b_{2}y_{n-3}+b_{3}}{b_{4}x_{n-1}y_{n-3}+b_{5}}, where the initial conditions $x_{-3},$ $x_{-2},$ $x_{-1},$ $x_{0},$ $y_{-3},$ $y_{-2},$ $y_{-1}$ and $y_{0}$ are arbitrary nonzero real numbers and $a_{i}$ and $b_{i}$ for $i=1,2,3,4,5$ are arbitrary real numbers. Also, we give some numerical examples to illustrate our results.