On Some Solvable Systems of Some Rational Difference Equations of Third Order

Our aim in this paper is to obtain formulas for solutions of rational difference equa-tions such as xn+1 = 1 +/- (x(n-1)y(n))/(1 - y(n)), y(n+1) = 1 = (y(n-1)x(n))/(1 - x(n)), and x(n+1) = 1 +/- (x(n-1)y(n-2))/(1- y(n)), y(n+1) = 1 +/- (y(n-1)x(n-2))/(1 - x(n)), where the initial conditions x(-2), x(-1), x(0), y(-2), y(-1), y(0) are non-zero real numbers. In addition, we show that the some of these systems are peri-odic with different periods. We also verify our theoretical outcomes at the end with some numerical applications and draw it by using some mathematical programs to illustrate the results.