Global and Local Behavior of the System of Piecewise Linear Difference Equations x n +1 = | x n | − y n − b and y n +1 = x n − | y n | + 1 Where b ≥ 4

The aim of this article is to study the system of piecewise linear difference equations x n + 1 = | x n | − y n − b and y n + 1 = x n − | y n | + 1 where n ≥ 0 . A global behavior for b = 4 shows that all solutions become the equilibrium point. For a large value of | x 0 | and | y 0 | , we can prove that (i) if b = 5 , then the solution becomes the equilibrium point and (ii) if b ≥ 6 , then the solution becomes the periodic solution of prime period 5.