The modified lanchester’s model of fighting
The mathematical model for the system description of military operations in the conditions of highly organized fight is developed. The General case of dependence of efficiency on time, characteristics of opposing units, dependence of superiority coefficient on time is considered. The system of differential inequalities is applied to receiving a recurrent formula. The recurrent formula is used to calculate the average number of sides, to estimate the main characteristics of the system (the necessary number of means, the time required to obtain the given numbers, the change in the coefficient of superiority of one side over the other depending on time). The efficiency of the sides is considered for any functional time dependence for continuous and discrete cases. The coefficient of superiority also depends on the time. For a small time interval in the model, it is possible to actually continuously monitor the change in the mean numbers. Efficiency of the parties and coefficients of superiority are considered as function of time. It is shown that the left and right bounds of interval estimates for the mean numbers have close values for the maximum and minimum efficiencies that differ little from each other. The error of result makes small percent.
Marked graph, a Poisson stream, density, efficiency, Markov process, a recurrent formula, superiority coefficient.
