EQUILIBRIUM POINT AND PERIODIC WITH PERIOD 5 OF A SYSTEM OF DIFFERENCE EQUATIONS

In this paper we study a two-dimensional piecewise linear system of difference equations. Initial conditions are negative x axis. We found a unique equilibrium point and two 5 cycles in the system. We separate the axis into intervals and we used direct calculations and single inductive statement in each interval of the axis to describe all behaviors in each interval of initial condition. Behaviors of solution to the system depend on choosing initial condition. It is either eventually equilibrium point or eventually prime period 5. This results could extent to understand global behaviors of family in piecewise linear system of difference equations.