The expressions and behavior of solutions for nonlinear systems of rational difference equations

Abstract

In this paper, we investigate the form of the solutions of the following systems of difference equations of second order xn+1xn+1==xnyn−1xn+yn,yn+1=xn−1ynxn+yn,xnyn−1xn−yn,yn+1=xn−1ynxn−yn, n=0,1,...,xn+1=xnyn−1xn+yn,yn+1=xn−1ynxn+yn,xn+1=xnyn−1xn−yn,yn+1=xn−1ynxn−yn, n=0,1,..., where the initial conditions x−1, x0, y−1 x−1, x0, y−1 and y0 y0 are arbitrary nonzero real numbers.

Keywords

• boundedness
• system of difference equations
• periodic solution