Research for Lanchester Models and Methods

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Irreducible Semi-Autonomous Adaptive Combat (ISAAC): An Artificial - Life Approach to Land Warfare
August 1, 1997
This study is a follow-on effort to a recently completed project, sponsored by the Commanding General, Marine Corps Combat Development Command, that assessed the general applicability of the new sciences to land warfare. 'New Sciences' is a catch-all phrase that refers to the tools and methodologies used in nonlinear dynamics and complex systems theory to study physical systems that exhibit a 'complicated dynamics.' CNA is currently developing a multiagent-based simulation of notional combat called ISAAC (Irreducible Semi-Autonomous Adaptive Combat), a preliminary version of which is described in this report. ISAAC takes a bottom-up, synthesist approach to the modeling of combat, vice the more traditional top-down, or reductionist approach.
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Land Warfare and Complexity, Part I: Mathematical Background and Technical Sourcebook
July 1, 1996
The purpose of this paper is to provide the theoretical framework and mathematical background necessary to understand and discuss the various ideas of nonlinear dynamics and complex system theory to plant seeds for a later, more detailed discussion (provided in Part II of this report) of how these ideas might apply to land warfare issues. This paper is also intended to be a general technical sourcebook of information. The main idea put forth in this paper is that significant new insights into the fundamental processes of land warfare can be obtained by viewing land warfare as a complex adaptive system. That is to say, by viewing a military 'conflict' as a nonlinear dynamical system composed of many interacting semi-autonomous and hierarchically organized agents continuously adapting to a changing environment. See also CRM 96-68.
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FLUCTUATIONS IN SYSTEMS WITH MULTIPLE STEADY STATES APPLICATION TO LANCHESTER EQUATIONS
February 1, 1981

This paper considers the effects of small random perturbations on deterministic systems of differential equations. The systems of interest have a steady state that is a saddle point. A first exit problem is formulated. The quantity of basic interest is the probability of exit from a band around the deterministic separatrix through a specified boundary, conditioned on initial position. A technique for the approximate calculation of this probability is given. As an example, it is shown how the theory applies to the calculation of the probability of victory in a combat situation that has a stochastic component.

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Methods of Operations Research
June 1, 1974
In World War II, the phrase 'operations research' has come to describe the scientific, quantitative study of operations of war. This report is a first attempt to describe some of the methods which have proved most valuable in the study of warfare, and to indicate possible fruitful lines for further development, military and nonmilitary. The first chapter outlines the scope and methods of the subject. The second chapter discusses the relevant portions of the theory of probability, which is the field of mathematics most useful for this work. The rest of the chapters discuss techniques which have been particularly useful, with illustrations picked from work done in the recent war.
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