Periodic Solutions of a System of Piecewise Linear Difference Equations

Wirot Tikjha*; Evelina Lapierre

doi:10.5666/KMJ.2020.60.2.401

Article

Kyungpook Mathematical Journal 2020; 60(2): 401-413

Published online June 30, 2020

Periodic Solutions of a System of Piecewise Linear Difference Equations

Wirot Tikjha*, Evelina Lapierre

Faculty of Science and Technology, Pibulsongkram Rajabhat University, Phitsanu- lok, Thailand 65000, Centre of Excellence in Mathematics, PERDO, CHE, Thailand
e-mail : wirottik@psru.ac.th
Department of Mathematics, Johnson and Wales University, 8 Abbott Park Place, Providence, RI, USA
e-mail : Evelina.Lapierre@jwu.edu

Received: June 28, 2017; Revised: September 2, 2019; Accepted: August 27, 2019

Abstract

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Abstract

In this article we consider the following system of piecewise linear difference equations: x_n₊₁ = |x_n| − y_n − 1 and y_n₊₁ = x_n + |y_n| − 1. We show 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.

Keywords: difference equation, periodic solution, stability