Modeling of the stochastic dynamics of changes in node states and percolation transitions in social networks with self-organization and memory

This paper explores the use of theoretical informatics applied for analyzing and modeling the processes in sociotechnical systems (social networks). A stochastic model of users' (network nodes) dynamic changes of states (opinions or moods) and the percolation threshold in a social network with random connections among nodes was developed. This model demonstrates the opportunity for jump-like transitions in states (opinions, moods) of the nodes in a social network over a short period of time without external influence. While developing the model, the probabilistic schemes of state-to-state transitions of nodes (users having certain opinions and views) were considered; a second-order nonlinear differential equation was derived; the boundary for calculating the probability density function for a system being in a certain state depending on the time interval was formulated. The differential equation of the model contains a member representing the opportunity for self-organization; it also considers the presence of memory. The results of analysis of the stochastic model support those previously obtained by the authors when investigating social network processes using the percolation theory. This theory was used for defining the time of reaching the threshold values for the share of social network nodes when certain opinions or preferences can spread freely within the whole social network.