Analysis of Combat Models Via Differential Equations

Abstract

During the First World War F. W. Lanchester made up a mathematical model for a combat situation to describe the attrition of two hostile homogeneous forces (a homogeneous force is a force including only one type of military units), both fighting with the knowledge of full tactical information (it means that an arbitrary operational unit is at any time able to detect at least that many hostile operational units as it is capable of eliminating). Over the years there have been many analyses and extensions of the Lanchester model such as guerilla model or mixed combat model. In this study we describe and analyse these models with differential equations and we examine the chance of prevailing in combat via historical battles. Today the system dynamics models of combat are a fairly supported research area by NATO.