Modeling Sociodynamic Processes Based on the Use of the Differential Diffusion Equation with Fractional Derivatives
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...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-02-01
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| Series: | Information |
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| Online Access: | https://www.mdpi.com/2078-2489/14/2/121 |
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| author | Liliya A. Demidova Dmitry O. Zhukov Elena G. Andrianova Alexander S. Sigov |
| author_facet | Liliya A. Demidova Dmitry O. Zhukov Elena G. Andrianova Alexander S. Sigov |
| author_sort | Liliya A. Demidova |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-11T08:39:53Z |
| format | Article |
| id | doaj.art-89dead5f98814c8aa4b373784023389b |
| institution | Directory Open Access Journal |
| issn | 2078-2489 |
| language | English |
| last_indexed | 2024-03-11T08:39:53Z |
| publishDate | 2023-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Information |
| spelling | doaj.art-89dead5f98814c8aa4b373784023389b2023-11-16T21:12:36ZengMDPI AGInformation2078-24892023-02-0114212110.3390/info14020121Modeling Sociodynamic Processes Based on the Use of the Differential Diffusion Equation with Fractional DerivativesLiliya A. Demidova0Dmitry O. Zhukov1Elena G. Andrianova2Alexander S. Sigov3Institute of Information Technologies, Federal State Budget Educational Institution of Higher Education, MIREA–Russian Technological University, 78, Vernadsky Avenue, 119454 Moscow, RussiaInstitute of Cybersecurity and Digital Technologies, Federal State Budget Educational Institution of Higher Education, MIREA–Russian Technological University, 78, Vernadsky Avenue, 119454 Moscow, RussiaInstitute of Information Technologies, Federal State Budget Educational Institution of Higher Education, MIREA–Russian Technological University, 78, Vernadsky Avenue, 119454 Moscow, RussiaInstitute for Advanced Technologies and Industrial Program, Federal State Budget Educational Institution of Higher Education, MIREA–Russian Technological University, 78, Vernadsky Avenue, 119454 Moscow, RussiaThis 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.https://www.mdpi.com/2078-2489/14/2/121sociodynamic processesuser activity on online media outletstime seriesthe Hurst exponentfractality of time seriesdifferential equations with fractional derivatives |
| spellingShingle | Liliya A. Demidova Dmitry O. Zhukov Elena G. Andrianova Alexander S. Sigov Modeling Sociodynamic Processes Based on the Use of the Differential Diffusion Equation with Fractional Derivatives Information sociodynamic processes user activity on online media outlets time series the Hurst exponent fractality of time series differential equations with fractional derivatives |
| title | Modeling Sociodynamic Processes Based on the Use of the Differential Diffusion Equation with Fractional Derivatives |
| title_full | Modeling Sociodynamic Processes Based on the Use of the Differential Diffusion Equation with Fractional Derivatives |
| title_fullStr | Modeling Sociodynamic Processes Based on the Use of the Differential Diffusion Equation with Fractional Derivatives |
| title_full_unstemmed | Modeling Sociodynamic Processes Based on the Use of the Differential Diffusion Equation with Fractional Derivatives |
| title_short | Modeling Sociodynamic Processes Based on the Use of the Differential Diffusion Equation with Fractional Derivatives |
| title_sort | modeling sociodynamic processes based on the use of the differential diffusion equation with fractional derivatives |
| topic | sociodynamic processes user activity on online media outlets time series the Hurst exponent fractality of time series differential equations with fractional derivatives |
| url | https://www.mdpi.com/2078-2489/14/2/121 |
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