Complete asymptotic analysis of a two-nation arms race model with piecewise constant nonlinearities
type: Item
instance of: scholarly article
title: Complete asymptotic analysis of a two-nation arms race model with piecewise constant nonlinearities
zbMATH Open document ID: 1233.91222
DOI: 10.1155/2012/745697
author: Chengmin Hou
author: Sui Sun Cheng
published in: Discrete Dynamics in Nature and Society
publication date: 2012-03-13T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 91B99
Mathematics Subject Classification ID: 91B55
zbMATH DE Number: 6014539
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/745697
OpenAlex ID: W1977686503
Wikidata QID: Q58700744
cites work: Complete asymptotic analysis of a nonlinear recurrence relation with threshold control
cites work: Complete asymptotic and bifurcation analysis for a difference equation with piecewise constant control
cites work: All solutions of a class of difference equations are truncated periodic
cites work: Perfect Equilibrium in a Model of Competitive Arms Accumulation
description: scientific article; zbMATH DE number 6014539