The aim of the present work is the calculation of the surviving combat units of three tactical engagements of homogeneous forces. For this purpose, we describe the deterministic mathematical models for tactical engagements of heterogeneous forces between regular military forces. It should be noted that a homogeneously armed military power is held by a type of weapon system, e.g. tanks. These models assume that there is a positive number expressing the firepower of the military units, as well as how the two forces have equivalent efficacy in the use of weapons systems. These models are of theoretical interest and describe ancient battles, while failing to reflect modern military conflicts. Instead, heterogeneously forces have different attrition rates, which are defined by the type of weapons, the types of enemy targets and various factors.
Keywords: model of warfare; Lanchesterís equation; differential equations