Existence and global attractivity of periodic solutions in a max-type system of difference equations

We consider in this paper the following system of difference equations with maximum x(n+ 1) = max{f1(n, x(n)), g1(n, y(n))} , n = 0, 1, 2, . . . , y(n+ 1) = max{f2(n, x(n)), g2(n, y(n))} where fi, gi , i = 1, 2, are real-valued functions with periodic coefficients. We use the Banach fixed point theorem to get a sufficient condition under which this system admits a unique periodic solution. Moreover, we show that this periodic solution attracts all the solutions of the current system. Some examples are also given to illustrate our results.