Dynamical instability in combat models: Computer arithmetic and mathematical models of attrition and reinforcement

Foremost, this paper reports a methodology that can be used to assess information gain and the value of information in combat operations. Secondly, the experiments discussed in this report give modest insight into underlying relationships between tactical intelligence information and combat results. Finally, the paper reports a unique application of information theory to measure intelligence information concerning the size and disposition of enemy forces. Combat models, nonlinear deterministic models of decision making processes, that deal with attrition of opposing forces, may contain dynamical instabilities and structural variance. Chaos in computation is one cause of instabilities in computer simulations of combat. Another cause of instabilities in decision processes is attributed to timing problems that arise when thresholds are crossed. An example of computer arithmetic effects for Patriot missile software is given in which very small timing errors accumulate and cause gross errors in detection and ranging. Several simple mathematical models of attrition and reinforcement are given and analyzed for chaotic behavior and nonlinear effects. Nonmonotonicity is demonstrated in the response of battle outcomes to changes in resources.