Complete Asymptotic Analysis of a Two-Nation Arms Race Model with Piecewise Constant Nonlinearities
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...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2012/745697 |
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| _version_ | 1832548503807590400 |
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| author | Chengmin Hou Sui Sun Cheng |
| author_facet | Chengmin Hou Sui Sun Cheng |
| author_sort | Chengmin Hou |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-ea7d9f262d2649729824ecc1a204b178 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-ea7d9f262d2649729824ecc1a204b1782025-02-03T06:13:58ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2012-01-01201210.1155/2012/745697745697Complete Asymptotic Analysis of a Two-Nation Arms Race Model with Piecewise Constant NonlinearitiesChengmin Hou0Sui Sun Cheng1Department of Mathematics, Yanbian University, Yanji 133002, ChinaDepartment of Mathematics, Tsing Hua University, Hsinchu 30043, TaiwanA 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.http://dx.doi.org/10.1155/2012/745697 |
| spellingShingle | Chengmin Hou Sui Sun Cheng Complete Asymptotic Analysis of a Two-Nation Arms Race Model with Piecewise Constant Nonlinearities Discrete Dynamics in Nature and Society |
| title | Complete Asymptotic Analysis of a Two-Nation Arms Race Model with Piecewise Constant Nonlinearities |
| title_full | Complete Asymptotic Analysis of a Two-Nation Arms Race Model with Piecewise Constant Nonlinearities |
| title_fullStr | Complete Asymptotic Analysis of a Two-Nation Arms Race Model with Piecewise Constant Nonlinearities |
| title_full_unstemmed | Complete Asymptotic Analysis of a Two-Nation Arms Race Model with Piecewise Constant Nonlinearities |
| title_short | Complete Asymptotic Analysis of a Two-Nation Arms Race Model with Piecewise Constant Nonlinearities |
| title_sort | complete asymptotic analysis of a two nation arms race model with piecewise constant nonlinearities |
| url | http://dx.doi.org/10.1155/2012/745697 |
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