On the global behaviour of a system of piecewise linear difference equations (Q2113760)

Summary: In a previous paper we considered the system \(x_{n+1} = |x_n| - y_n - 1\) and \(y_{n+1} = x_n + |y_n| - 1\) 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 \(\mathbb{R}^2\) then the solution is the equilibrium point, one of two prime period-3 solutions, or one of two prime period-4 solutions.