A CONTRIBUTION TO THE THEORY OF MANAGING THE NUMBER OF NON-PROFIT ORGANIZATIONS IN RUSSIA
A qualitative theory of the dynamics of the number of people involved in non-profit organizations (NPOs) in the Russian Federation (RF) is built on the basis of mathematical methods of system analysis. Differential equations for the relative rate of growth in the number of people in the NPO sphere are presented. Two groups of deterministic differential equations to represent the dynamics of the total number of people in NPOs are considered: ordinary differential equations in which the relative growth rate is a function of the number of people not covered by the sphere of NPOs, and equations where the relative speed is a function of time. The solution of the differential equation of the first group yields an analytical dependence for the relative growth of people in the field of NPOs, which allows predicting a temporal behavior of a variable, as well as theoretically justifying the choice of a functional dependence of the relative growth rate of the number of people when obtaining and analyzing the equations of the second group. In the equations of the second group: , an increase in the total number of people covered by the sphere of NPOs is normalized by - the point where an increase in the number of people in NPOs stops. When the equation transforms into an equation of exponential type. The exact solution of the given equation has the form of a Gaussian distribution curve. The applicability of the equation to describe the dynamics of the total number of people in the NPO sphere indicates that the evolution of the socio-economic system can be viewed as its transition from a less probable state to a more certain, following the Gaussian curve. Thus, our theoretical approach allows us to produce the quantitative description of the dynamics of the socio-economic system from the standpoint of the theory of random processes. The results of the theoretical analysis can be used in the construction of a simulation model of the dynamics of changes in the number of NPOs, with the aim of further research into the effects of NPO activity on experimentally measured indicators of the population’s life quality.