Modeling the Dynamics of User’s Mood Based on the Fokker-Planck Equation and Changes in the Parameters of Network Graphs of Their Comments

Abstract

The paper studies the dynamics of the moods of Internet media users based on the Fokker-Planck equation and changes in the parameters of the graphs of networks of their comments. The article introduces the concept of the base state vector of the comment network graph, the elements of which are: the average value of the mediation coefficient, the average value of the clustering coefficient, the proportion of users in a particular state. The time dependence of the distance between the base vector and the current state vector forms a time series whose x-values can be thought of as a “wander point”. This time series is considered on the segment [Lmin, Lmax], where Lmin и Lmax – given boundaries of the interval of possible values of the network state. The current state of the comment graph can be determined using network analysis tools and text analysis methods. The solution of the Fokker-Planck equation made it possible to obtain an analytical time dependence of the probability density of detecting the value of the state of the network in one or another value x. Based on this approach, an algorithm can be created for predicting the time to reach a given state of the user comments network graph (the allowable distance between the base and observed vectors) for a given probability level (this allows time to be predicted). Analysis of the model showed its adequacy, not inconsistency.