On the system of two nonlinear difference equations <mml:math alttext="$x_{n

Abstract

We study the oscillatory behavior, the periodicity and the asymptotic behavior of the positive solutions of the system of two nonlinear difference equationsxn+1=A+xn−1/ynandyn+1=A+yn−1/xn, whereAis a positive constant, andn=0,1,….