Abstract
In this paper, we deal with the existence of solutions and the periodicity character of the following systems of rational difference equations with order three:
x(n+1) = x(n)y(n-2)/y(n-1)(+/- 1 +/- x(n)y(n-2)), y(n+1) = y(n)x(n-2)/x(n-1)(+/- 1 +/- y(n)x(n-2)),
where the initial conditions x(-2), x(-1), x(0), y(-2), y(-1) and y(0) are nonzero real numbers.