Advances in Difference Equations
Volume 2010 (2010), Article ID 573281, 14 pages
doi:10.1155/2010/573281
Research Article

On the Global Character of the System of Piecewise Linear Difference Equations 𝑥 𝑛 + 1 = | 𝑥 𝑛 | − 𝑦 𝑛 − 1 and 𝑦 𝑛 + 1 = 𝑥 𝑛 − | 𝑦 𝑛 |

Wirot Tikjha,1,2 Yongwimon Lenbury,1,2 and Evelina Giusti Lapierre3

1Department of Mathematics, Faculty of Science, Mahidol University, Rama 6 Road Bangkok, 10400, Thailand
2Center of Excellence in Mathematics, PERDO Commission on Higher Education, Si Ayudhya Road, Bangkok 10400, Thailand
3John Hazen White School of Arts and Sciences, Department of Mathematics, Johnson and Wales University, 8 Abbott Park Place, Providence, RI 02903, USA

Received 23 June 2010; Revised 4 September 2010; Accepted 2 December 2010

Academic Editor: Donal O'Regan

Copyright © 2010 Wirot Tikjha et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider the system in the title where the initial condition ( 𝑥 0 , 𝑦 0 ) ∈ 𝐑 2 . We show that the system has exactly two prime period-5 solutions and a unique equilibrium point ( 0 , − 1 ) . We also show that every solution of the system is eventually one of the two prime period-5 solutions or else the unique equilibrium point.