Equilibrium Point and Prime Period 4 in Certain Piecewise Linear System of Difference Equation

Abstract

In this article we consider two-dimensional first order piecewise linear systems of difference equations. We are specific initial conditions of solutions in some parts of x axis. Equilibrium point and 4 cycles are observed in each system. We use direct calculations to show characters of the systems and then restrict that part of x axis and use single inductive statement to describe all behaviors in each system. Behaviors of each system depend on initial condition. It is either eventually equilibrium point or eventually prime period 4. We can determine that which parts of x axis make solution being equilibrium point or periodic with period 4. This results will be pieces of information to understand global behaviors of?? family in piecewise linear system of difference equations.