ABSTRACT
In this chapter, the author gives an introduction to some simple mathematical models of combat, including their own Adaptive Dynamic Model. Theoretical biologists concerned with morphogenesis—the development of pattern—is, in some cases, situated similarly. Theoreticians seek simple models that will generate a reasonable menu of core qualitative behaviors: threshold eruptions, persistence at endemic levels, recurrence in cycles, perhaps chaotic dynamics. The aim is to produce transparent, parsimonious models that will generate the core menu of gross qualitative system behaviors. The eclectic English engineer made contributions to diverse fields, including automotive design and the theory of aerodynamics. He is best remembered for his equations of war, appropriately dubbed the Lanchester equations. The Lanchester square system captures the predation benefit but completely ignores the prey cost of density. The whole dynamic, while driven by myriad political and military-industrial interests on all sides, was certainly supported by Lanchester's innocent-looking linear differential equations.
