Analyzing and forecasting the dynamics of Internet resource user sentiments based on the Fokker–Planck equation - J. P. Perova; S. A. Lesko; A. A. Ivanov (Российский технологический журнал)
Objectives. The study aims to theoretically derive the power law observed in practice for the distribution of characteristics of sociodynamic processes from the stationary Fokker–Planck equation and apply the non-stationary Fokker–Planck equation to describe the dynamics of processes in social systems.Methods. During the research, stochastic modeling methods were used along with methods and models derived from graph theory, as well as tools and technologies of object-oriented programming for the development of systems for collecting data from mass media sources, and simulation modeling approaches.Results. The current state of the comment network graph can be described using a vector whose elements are the average value of the mediation coefficient, the average value of the clustering coefficient, and the proportion of users in a corresponding state. The critical state of the network can be specified by the base vector. The time dependence of the distance between the base vector and the current state vector forms a time series whose values can be considered as the “wandering point” whose movement dynamics is described by the non-stationary Fokker–Planck equation. The current state of the comment graph can be determined using text analysis methods.Conclusions. The power law observed in practice for the dependence of the stationary probability density of news distribution by the number of comments can be obtained from solving the stationary Fokker–Planck equation, while the non-stationary equation can be used to describe processes in complex network structures. The vector representation can be used to describe the comment network states of news media users. Achieving or implementing desired or not desired states of the whole social network can be specified on the basis of base vectors. By solving the non-stationary Fokker–Planck equation, an equation is obtained for the probability density of transitions between system states per unit time, which agree well with the observed data. Analysis of the resulting model using the characteristics of the real time series to change the graph of comments of users of the RIA Novosti portal and the structural parameters of the graph demonstrates its adequacy.