Elsayed M. Elsayed

Our aim in this paper is to obtain formulas for solutions of rational difference equations such as xn+1=1±xn−1yn/1−yn,yn+1=1±yn−1xn/1−xn, and xn+1=1±xn−1yn−2/1−yn,yn+1=1±yn−1xn−2/1−xn, where the initial conditions x−2, x−1, x0, y−2, y−1, y0 are non-zero real numbers. In addition, we show that the some of these systems are periodic 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.

In the present paper, we prove the boundedness of the positive solutions as well as local and global asymptotic stable of the equilibrium points of difference equations system in the second order Furthermore, we study the solutions for three special cases of system. Numerical examples are provided to illustrate results.