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

Authors: Evelina Lapierre; Wirot Tikjha

Addresses: Department of Mathematics, Johnson and Wales University, 8 Abbott Park Place, Providence, RI, 02903, USA ' Faculty of Science and Technology, Pibulsongkram Rajabhat University, Phitsanulok, 65000, Thailand

Abstract: 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 ℝ² then the solution is the equilibrium point, one of two prime period-3 solutions, or one of two prime period-4 solutions.

Keywords: difference equation; dynamical system; periodic solution; stability.

DOI: 10.1504/IJDSDE.2021.117371

International Journal of Dynamical Systems and Differential Equations, 2021 Vol.11 No.3/4, pp.341 - 358

Received: 01 Jul 2020
Accepted: 02 Mar 2021
Published online: 01 Sep 2021 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article