Complex dynamics and control of arms race |
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| Institution: | 1. Carnegie Mellon University, H. John Heinz III College of Public Policy & Management, 5000 Forbes Avenue, Pittsburgh, PA 15213-3890, USA;2. Department for Operations Research and Control Systems, Institute for Mathematical Methods in Economics, Vienna University of Technology, Argentinierstr. 8/105-04, 1040 Vienna, Austria;3. Wittgenstein Centre for Demography and Global Human Capital (IIASA, VID/ÖAW, WU), Vienna Institute of Demography/Austrian Academy of Sciences, Wohllebengasse 12-14, 1040 Vienna, Austria;4. Department of Business Administration, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria;5. Department of Econometrics and Operations Research & CentER, Tilburg University, PO Box 90153, 5000 LE Tilburg, The Netherlands;6. Department of Economics, University of Antwerp, Prinsstraat 13, 2000 Antwerp, Belgium;1. Department of Animal Science, University of Zanjan, Zanjan 45371-38791, Iran;2. Department of Animal Sciences, North Dakota State University, Fargo, ND 58108, USA |
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| Abstract: | The aim of this paper is to show that asymmetric, nonlinear armament strategies may lead to chaotic motion in a discrete-time Richardson-type model on the arms race between two rival nations. Local bifurcation analysis reveals that ‘complicated’ dynamics will only occur if neither nation has an absolute advantage over the other one with respect to its level of armament and its capability to keep up the expenditures on armament. The calculation of Lyapunov exponents supports the existence of chaos. Since transitions to chaos can be identified with transitions to war, we use the Ott-Grebogi-Yorke-algorithm to stabilize the arms race model in the chaotic regime and improve the system's performance by making very small time-dependent changes of a parameter under control. |
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