Modeling Sociodynamic Processes Based on the Use of the Differential Diffusion Equation with Fractional Derivatives

Abstract

This paper explores the social dynamics of processes in complex systems involving humans by focusing on user activity in online media outlets. The R/S analysis showed that the time series of the processes under consideration are fractal and anti-persistent (they have a short-term memory and a Hurst exponent significantly less than 0.5). Following statistical processing, the observed data showed that there is a small amount of asymmetry in the distribution of user activity change amplitudes in news comments; the amplitude distribution is almost symmetrical, but there is a heavy tail as the probability plots lie above the normal probability plot. The fractality of the time series for the observed processes could be due to the variables describing them (the time and level of a series), which are characterized by fractional variables of measurement. Therefore, when figuring out how to approximate functions to determine the probability density of their parameters, it is advisable to use fractional differential equations, such as those of the diffusion type. This paper describes the development of such a model and uses the observed data to analyze and compare the modeling results.