Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 745697, 17 pages
Research Article

Complete Asymptotic Analysis of a Two-Nation Arms Race Model with Piecewise Constant Nonlinearities

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

Received 30 August 2011; Accepted 25 October 2011

Academic Editor: Guang Zhang

Copyright © 2012 Chengmin 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.


A discrete time two-nation arms race model involving a piecewise constant nonlinear control function is formulated and studied. By elementary but novel arguments, we are able to give a complete analysis of its asymptotic behavior when the threshold parameter in the control function varies from 0+ to . We show that all solutions originated from positive initial values tend to limit one or two cycles. An implication is that when devastating weapons are involved, “terror equilibrium” can be achieved and escalated race avoided. It is hoped that our analysis will provide motivation for further studying of discrete-time equations with piecewise smooth nonlinearities.