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Zbl 1233.91222
Hou, Chengmin; Cheng, Sui Sun
Complete asymptotic analysis of a two-nation arms race model with piecewise constant nonlinearities. (English)
[J] Discrete Dyn. Nat. Soc. 2012, Article ID 745697, 17 p. (2012). ISSN 1026-0226; ISSN 1607-887X/e

Summary: 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 $\infty$. 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.

MSC 2000:: *91B99 Mathematical economics
91B55

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