Uncertainty Conditions and Time Delay in Lanchester’s Combat Models

abstract

English

F. W. Lanchester originally published his mathematical model for air to air combat [1,2]. There are three main types of such systems: “direct fire” model, model “guerilla warfare” and so-called “mix warfare” model. These models known as the linear and square law became the basis for much of the analysis of combat. These differential equations models have been the methodology to present and solve many historical combat models. All these models are well studied in the continuous case. In the end of XX many scientists alluded to difficulties in solving more difficult “realistic” equations and suggested numerical methods that can easily and conveniently be numerically solved on a computer. The use of computers to analytically solve or numerically solve combat models is the standard method. Discrete dynamical system (difference equations) as the discrete form of Lanchester’s equations in combat models start to use and study at the beginning of XXI [3]. Some works in this direction were conducted in TSNUK, Kyiv, Ukraine as the bachelor’s theses in 2015, 2016. This report is a continuation of the research [4] and devoted to new problem in such kind models, namely: - the presence delay in the equations when we have case of belated reaction of one of the sides of the battle - the presence of interval uncertainty in coefficients of the models.

Lanchester’s models, economic models, delay

NOVOTNÁ, V.; PŮŽA, B.; SHATYRKO, A.

27. 8. 2018

Praha

12

13

2