The System of two Difference Equations xn+1 = (p+ yn−k)/yn, yn+1 = (q + xn−k)/xn

Abstract In this paper we study the boundedness, the periodicity and the asymptotic behavior of the positive solutions of the system of difference equations

xn+1 = p+ yn−k

yn , yn+1 =

q + xn−k xn

,

where p, q are positive constants, k ∈ {2, 3, ...} and the initial conditions x−k, y−k, ..., x0, y0 are positive numbers.