Group behavior modeling based on: stochastic cellular automata with variable memory, systems of differential kinetic equations and analysis of social processes' time series

摘要

The paper considers a set of models for the description, analysis, and modeling of group behavior by user actions in complex social systems. In particular, electoral processes in which preferences are selected from several possible ones can be considered. The dynamics of changes in the preferences of voters can be described graphically diagram of possible transitions between States, on the basis of which it is possible to obtain a system of differential kinetic equations describing the process. The analysis of decisions shows the possibility of existence within the model, different modes of change of preferences of voters. In addition, the paper describes the developed model of stochastic cellular automata with variable memory, in which 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 it 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 a given number of memory steps. After the number of steps equal to the depth of memory, its transition to the type that had the maximum value of its amount occurs. The effect of external factors (such as media) on changes in node types can be set for each step using a transition probability matrix. Processing of sociological data of the electoral campaign of 2015-2016 at the choice of the USA President using the method of almost - periodic functions allowed to estimate the parameters of the complex of created 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. Some sets of coefficients in differential equations and cellular automata models show oscillating and almost - periodic changes in the preferences of voters, which largely coincides with real observations.