We present numerical results from a nonlinear dynamical model with discrete time that simulates the implications of ballistic missile defense systems (SDI) on the arms race between the two superpowers. As dynamical variables we introduce the number of intercontinental ballistic missiles (ICBMs), antiballistic missile systems (ABMs) and anti-ABM systems such as antisatellite weapons (ASAT) of each of the two sides. The time evolution of these systems (arms race) is simulated numerically under various parameter assumptions (scenarios). The a priori unpredictability of human decisions is simulated through random fluctuations of the buildup parameters. The results of our idealized model indicate that for most parameter combinations, the introduction of SDI systems leads to an extension of the offensive arms race rather than a transition to a defense-dominated strategic configuration. A reduction in the number of offensive weapons, that is, an approach to a defense-dominated strategy, was observed if either the number of reentry vehicles per ICBM (MIRV) is limited to much smaller values than presently realized or if the accuracy of offensive weapons is significantly reduced. For the case of a strongly accelerated arms buildup (either offensive or defensive), we observe a loss of stability of the solutions that we interpret as a transition to unpredictable chaos. We also incorporate a discussion of economic and risk parameters, both of which also tend to increase with the introduction of SDI systems.
A set of rules often invoked to explain or justify the evolution of intentions and the consequent behavior of competitive systems consists of the following: 1. The friend of my friend is my friend. 2. The friend of my enemy is my enemy. 3. The enemy of my friend is my enemy. 4. The enemy of my enemy is my friend. These rules have been modeled as a set of nonlinear, coupled differential equations from which predictions can be derived as to eventual alliance building or conflict in the system, predictions which are quite ominous for the behavior of simple three-body systems. This paper presents illustrations of the application of the rules to international behavior and discusses the relationship between the rules as usually verbally applied and the associated mathematical models. Not all of these rules are equally desirable: behavior in accordance to the fourth rule has led to major difficulties in the “real world.” This fourth rule cannot just be dropped, since the four rules are not independent of each other in the mathematical model. Hence the model must be altered. A simple mathematical modification is suggested which implies increased flexibility in the verbal statement and application of the rules; e.g., the fourth now reads “The enemy of my enemy may be my friend.” The altered model leads to altered predictions of the evolution of intent which are much less ominous for the outcome of three-body competitions.
Mankind has been going off to war for thousands of years, the planners and participants often proceeding with complete confidence in a successful outcome. Such confidence means that a win is predicted when initiating or responding to a battle, a campaign, or a war. Warriors and their societies knew that reverses were possible. However, given care, resources, and planning (e.g., given the initiative) they usually expected that they would come out ahead, after averaging over individual losses in a battle, individual battles in a campaign, or individual campaigns in a war. Given the choice, they did not start unless they could predict success -given the resources, timing, and strategies at their command. This article is about prediction; when it is possible, when it is not.Military historians have often pointed out the chaotic nature of battle and the likelihood that things often will not go according to plan: The Clausewitzean' 'fog of battle' obscured much. Still, generals initiated campaigns assuming that they could plan successfully for the statistical average. Over the centuries, historians have described how wars initiated by 'statesmen' have often turned out counter to the expectations of these statesmen. (If this were not the case, no initiator would ever have lost a war.) In fact, statesmen have often lost control of the process of going to war, slipping into disasterous conflicts against the desires of both sides.2 Still, over our long history, generals have prepared for and engaged in wars, statesmen have initiated, or tempted the initiation of wars. If the predictions turned out wrong, if expectations went awry, nations or societies of nations might be significantly altered or even destroyed. However, the fundamental presumption was always that basic civilization would be preserved, that human society would continue to 'progress' (this in spite of such counter examples as the thousand year decline of the West after the war wearied collapse of the Roman Empire).With the advent of modern science and technology and its application to war, many writers and military organizations soon lost sight of the possible lack of predictability.3 After all, the 'success' of modem, post-Galilean science is due to its ability to make prediction. The height of predictability was soon reached with the mathematization of strategy and tactics; mathematical models were created and applied to determine the outcomes of individual battles and campaigns.5 Even grander mathematical schemes were applied to the study of arms races and the initiation of wars.6 Many people, certainly most non-mathematicians, view mathematics as the acme of prediction; once axioms were accepted, necessary consequences
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