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

Abstract

The aim of this article is to study the system of piecewise linear difference equations xn+1=|xn|−yn−b and yn+1=xn−|yn|+1 where n≥0. A global behavior for b=4 shows that all solutions become the equilibrium point. For a large value of |x0| and |y0|, 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.