Alvin M. Saperstein

The “Long Peace”— Result of a Bipolar Competitive World?

One of the reasons advanced for the absence of a major war between the two superpowers during the forty-five years of their enmity since World War II is that the world system in which they functioned was essentially bipolar and hence, presumably, inherently more stable than previous multipolar worlds. Given the recent decline in the power of the U.S. and the U.S.S.R. relative to the rest of the world, it is important to test the validity of this presumption. A nonlinear mathematical model of international competition is presented in which the transition from predictable laminar to unpredictable turbulent flow is the model manifestation of the transition from cold to hot war in the world system being modelled. The model is a tripolar competition which arises continuously from a bipolar system as a coupling parameter is varied. Thus the realm of nonchaotic, stable, competition can be examined as a function of the coupling parameter. It is found that the regime of stability decreases as the system complexity increases. Thus the simple model lends credence to the presumption that a tripolar world is inherently less stable than the corresponding bipolar world.

A Nonlinear Dynamical Model of the Impact of SDI on the Arms Race

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.

Predictability, Chaos, and the Transition to War

* A. M. Saperstein is Professor of Physics, Department of Physics, Wayne State, University, Detroit, U.S.A.: and Chairman of the Center for Peace and Conflict Studies, Detroit Council for World Affairs. 1. War predictability, mathematics and the lessons of the past 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

Alliance Building versus Independent Action

An important international security question is whether nations in an anarchic competitive world system are more likely to ensure their security by pursuing policies of complete independence or of alliance building. The question is addressed using the paradigm that “strong chaos” in an arms-race model is equivalent to crisis instability and war in the international system being modeled. Nonlinear recursion relation models of competitive arms procurement are constructed for independent arming and for alliance building policies in a world system of three symmetric nations. The results are that alliance building always preserves a peaceful world from perturbations in the relationships between the competing member states whereas independent courses of action may allow such perturbations to build up to strong chaos and presumably war.

The Enemy of My Enemy Is My Friend Is the Enemy: Dealing with the War-Provoking Rules of Intent

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.

Chaos As A Tool For Exploring Questions of International Security

Mathematical models-static or dynamic-of international systems arc often used to predict outcomes of specific policy choices. The focus of this paper is not such predictions themselves but the question of whether or not such predictability is meaningful. Non-predictability in a deterministic dynamic model is usually referred to as “chaos” and is used in this paper as a paradigm for crisis instability and the possible outbreak of war in a system of competing states. The use of the paradigm is illustrated via initial explorations of three international security questions: 1.) Which is more stable, a bipolar or a multipolar system? 2.) Which are more war prone, democracies or autocracies? 3.) Which leads to more stability, seeking security via independent acquisition of arms or via a balance of power? A simple model-not empirically founded but manifesting some dominant aspects of the situation-is formulated for each question. The stability regime of each model is then determined. Using the postulate that a larger stability range indicates a less war-prone world, and vice-versa, answers to these questions are found, thus providing an alternate approach to the investigation of pressing theoretical and practical questions in international relations.

Fluid dynamic and kinetic theory models for a nonprovocative land defense of central Europe

A major problem in using theory to make predictions in a practical situation is the validity of the theory. The theoretical predictions are only as good as the theory. A model is developed, based upon a one‐dimensional equation of continuity, for predicting the effectiveness of an attritional mode of defense against a conventional land attack in Europe. The validity of the model and its predictions is tested by comparing the results with those of a stochastic, discrete model of multiple small defensive battles, with the latter results obtained by Monte Carlo type computer simulations. The concordance of the results supports the validity of the models and the efficacy of applying physical‐type reasoning to pressing, nonphysical, world problems.

Dynamical modeling of the onset of war

Predictive structure building - static and dynamic predictive modelling of arms races - static and dynamic dynamical concepts chaos and international stability - modelling war initiation combined models - capabilities and intentions past and future research.

A Comment on the Power Law Relation Between Frequency and Severity of Terrorist Attacks

Richardson first pointed out the power-law relation between the occurrence of war-like events and the consequent casualties. More recently, attention has been paid to the observed power-law relation between the frequency of terrorist acts and the number of resulting casualties and attempts have been made to explain these observations by deriving them from a model of randomly aggregating and disaggregating terrorist groups. This comment points out a weakness in the model and offers a simple extension to eliminate it.

Chaos in models of arms races and the initiation of war: Crisis stability and instability in an international system†

INTRODUCTION: THEORY AND POLICY MAKING S ometime during the “Cold War,” political scientists developed the complimentary concepts of crisis stability/crisis instability for describing the state of a competitive international system. They are best defined by illustrative examples. When a Soviet fighter aircraft shot down the civilian Korean airliner, KAL007, in Soviet airspace in September 1983, almost 300 lives were lost, including that of a US Congressman. Much international bluster resulted, but no war. Sixty-nine years earlier, in Sarajevo (then part of the Austrian-Hungarian Empire) two lives were lost in an assassination. The result was World War I, with an excess of 20 million lives lost. In the world system of 1983, a moderate perturbation remained moderate—the system was stable. In the world of 1914, a very minor perturbation of the system grew to a major disturbance, which destroyed the system. This earlier, crisis unstable, situation manifested “extreme sensitivity” to small perturbations of the system. This contrast between stability and instability in the international system sounds very much like the use of the same words in dynamical systems. In dynamics, a positive value for a Liapunov exponent for the system implies extreme sensitivity to perturbations which implies chaos. Those concerned with international security have always longed for an understanding of the transition of an international system from stability to instability. Such