On the global behaviour of a system of piecewise linear difference equations

In a previous paper we considered the system xn+1 = 'xn' − yn - 1 and yn+1 = xn + 'yn' − 1 and showed by mathematical induction that when the initial condition is an element of the closed second or fourth quadrant, the solution to the system is either a prime period-3 solution or one of two prime period-4 solutions. In this paper we complete the study of the global behaviour of the system. We show that when the initial condition is an element of ℝ2 then the solution is the equilibrium point, one of two prime period-3 solutions, or one of two prime period-4 solutions.