Choice of optimal levels of gravitation in social and economic systems based on the principles of gravitation

The paper presents the methods to find the optimal levels of gravitation (attraction) in the systems of the development, based on the principle of gravity (attraction) to a predetermined level at a fixed set of the parameters. As the main characteristics of the system development, the function of the number of subjects, reached a certain level of development of the whole set of indicators at a given time, is taken. Solutions of partial derivative equations derived earlier for the average number of entities in the system, having a given level of development, at any given time are proposed. As input parameters of the system, the paper considers a function describing the distribution of subjects with different levels of the given quality, the intensity of the training the subjects and the average intensity of the perception of the impact of the training subject. The formal tasks of choosing the optimal set of the levels of gravity (attraction) for a given set of readings are stated. The paper examines two variants of the objective function, the optimization of which takes place: the maximum total value of the level of development of all subjects at the end of the given period of routine and the maximum total value of the quantity over the interval routine. Based on the solutions of the equations, the general procedure for solving optimization problems is described. In the case of one level (of attraction) there is a complete solution of the task of the choice of the optimal level with the use of package MathCad.