Complex of Description Models for Analysis and Control Group Behavior Based on Stochastic Cellular Automata with Memory and Systems of Differential Kinetic Equations

This paper considers the complex of models for the description, analysis, and modeling of group behavior by user actions in complex social systems. In particular, electoral processes can be considered in which preferences are selected from several possible ones. For example, for two candidates, the choice is made from three states: for the candidate A, for candidate B and undecided (candidate C). Thus, any of the voters can be in one of the three states, and the interaction between them leads to the transition between the states with some delay time intervals, which are one of the parameters of the proposed models. The dynamics of changes in the preferences of voters can be described graphically on diagram of possible transitions between states, on the basis of which is possible to write a system of differential kinetic equations that describes the process. The analysis of the obtained solutions shows the possibility of existence within the model, different modes of changing the preferences of voters. In the developed model of stochastic cellular automata with variable memory at each step of the interaction process between its cells, a new network of random links is established, the minimum and the maximum number of which is selected from a given range. At the initial time, a cell of each type is assigned a numeric parameter that specifies the number of steps during which will retain its type (cell memory). The transition of cells between states is determined by the total number of cells of different types with which there was interaction at the given number of memory steps. After the number of steps equal to the depth of memory, transition to the type that had the maximum value of its sum occurs. The effect of external factors (such as media) on changes in node types can set for each step using a transition probability matrix. Processing of the electoral campaign's sociological data of 2015-2016 at the choice of the President of the United States using the method of almost-periodic functions allowed to estimate the parameters of a set of models and use them to describe, analyze and model the group behavior of voters. The studies show a good correspondence between the data observed in sociology and calculations using a set of developed models. Under some sets of values of the coefficients in the differential equations and models of cellular automata are observed the oscillating and almost-periodic character of changes in the preferences of the electorate, which largely coincides with the real observations.