On The Global Behaviour Of A System Of Piecewise Linear Difference Equations

In a previous paper we considered the system x(n+1) = vertical bar x(n)vertical bar- y(n) - 1 and y(n+1) = x(n) + vertical bar y(n)vertical bar - 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 R-2 then the solution is the equilibrium point, one of two prime period-3 solutions, or one of two prime period-4 solutions.