Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 492014, 10 pages
http://dx.doi.org/10.1155/2013/492014
Research Article

Bifurcation in a Discrete-Time Piecewise Constant Dynamical System

Chenmin Hou1 and Sui Sun Cheng2

1Department of Mathematics, Yanbian University, Yanji 133002, China
2Department of Mathematics, Tsing Hua University, Hsinchu, Taiwan 30043, China

Received 15 August 2012; Revised 27 February 2013; Accepted 28 February 2013

Academic Editor: Raghib Abu-Saris

Copyright © 2013 Chenmin Hou and Sui Sun Cheng. 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

The study of recurrent neural networks with piecewise constant transition or control functions has attracted much attention recently because they can be used to simulate many physical phenomena. A recurrent and discontinuous two-state dynamical system involving a nonnegative bifurcation parameter is studied. By elementary but novel arguments, we are able to give a complete analysis on its asymptotic behavior when the parameter varies from 0 to . It is hoped that our analysis will provide motivation for further results on large-scale recurrent McCulloch-Pitts-type neural networks and piecewise continuous discrete-time dynamical systems.