Use of Lotka-Volterra differential equations for the creation of the model of combat use of military formation in the mutual fire conditions

Abstract

The analysis of armed conflicts of recent decades suggests that the quantitative advantage in forces and means does not always ensure the successful completion of combat missions. Quite often, the organization of military formations combat use and enemy fire demage comes to the fore from the whole set of factors.The article considers the possibility of using Lotka-Voltair differential equations in creating a model of combat use of military formations in terms of fire interaction.These equations are widely used in the study of population growth dynamics of biological species under conditions of competition (when both parties are predators). The main hypotheses when using the above equations include the following: the supplies needed for growth are either available in unlimited quantities, or their income is strictly regulated over time; species harm each other, and per unit time the number of losses is always proportional to the probability of encountering individuals of these two species.The application of the Lotka-Voltair equations allows to determine the dynamics of changes in the level of military formation capabilities in the conditions of mutual fire influence of the parties and to determine the critical level of capabilities, and further, on the basis of this information to provide recommendations for changing certain constants.