Lanchester Models With Discontinuities: An Application to Networked Forces

Abstract

W e consider an extension of Lanchester's models of conflict by studying the effect of instantaneous, global reductions in effectiveness to include changes in the underlying process. We apply this extension to a hypothetical scenario based on the battle of Iwo Jima and discuss implications for networked forces.

Lanchester for cyber: The mixed epidemic-combat model

“…When do epidemic effects of malware need to be explicitly considered in a unified combat model? If the spread of the cyber infection is very fast compared to the combat process —for example, if the time until malware saturation is and the rate of blue attrition due to red action is on the order of 1 per min—then the disruption of the network may be adequately treated as a uniform, catastrophic failure; this situation is described in . Alternatively, if the spread of cyber infection is very slow, then the effect may be negligible and the attrition formulation alone is sufficient.…”

“…Deterministic combat models are a staple of Military Operations Research; for an overview see . Instantaneous malware spread in generalized Lanchester systems is explored in . For an overview of epidemic models, see .…”

“…These three models are developed and exercised with an instantaneous infection in . Our analysis will focus exclusively on aimed fire, where we believe that malware is most important.…”

Differential equation models for sharp threshold dynamics

“…A model applying these equations to the Ardennes campaign is in [7]. Combat models with a single, deterministic threshold are studied by Schramm [35].…”