Modeling of sociodynamic processes based on the use of a diffusion equation with fractional derivatives

K.K. Otradnov, D.I. Sabirova, D.O. Zhukov


On the example of the activity of users of network mass media, the sociodynamics of processes in complex systems with the participation of the human factor was considered. The time series of the studied processes are fractal in nature and have anti-persistence (they have a short-term memory; the Hurst exponent is less than 0.5). Statistical processing of the observed data showed that in the distribution of amplitudes of changes in user activity, an insignificant amount of asymmetry is noticed, the distribution of amplitudes is practically symmetrical; a “heavy tail” is also noted: the graphs of the density of distributions lie above the graph of the normal distribution. The fractality of the time series of the processes under study is due to the fact that the variables describing them are characterized by fractional measurement variables, which means that when deriving approximating probability density functions of the distribution of their parameters, it is appropriate to use fractional differential equations, for example, of the diffusion type. The article considers the construction of such a model, its analysis and comparison of the simulation results with the observed data.

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