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

Abstract

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.

Keywords

• difference equations
• periodicity nature
• system of difference equations