DOI: https://doi.org/10.15588/1607-3274-2020-2-13

RESEARCH OF DYNAMICS OF INFORMATION DISTRIBUTION PROCESSES BASED ON DIFFUSION HYBRID MODELS

E. V. Ivohin, L. T. Adzhubey, O. V. Gavrylenko, Yu. O. Naumenko

Abstract


Context. Solving of the problem of formalization and study of the development of the process of information dissemination over time and its impact on the society is very important for ensuring information security. It is necessary to use a fundamentally new tool that will adequately reflect the state of the dynamic component of the process of information dissemination.

Objective. The goal of the work is the research of mathematical models of processes of dissemination to model the dynamics of changes in the levels of influence of information within different target groups.

Method. This paper proposes an approach to formalize hybrid mathematical models of the dynamics of information process propagation in the target group on the basis of diffusion models. In order to improve the adequacy and reliability of the results obtained from the constructed models, it is proposed to apply hybrid systems based on diffusion models and dynamic models describing the process of changing the size of the contingent of the information dissemination environment. The proposed method allows to simulate the dynamic processes of observing the level of information impact based on the solution of inhomogeneous diffusion equations, the change of intervals of a spatial variable in which is determined by additional relations in the form of a system of differential equations. The scalar case of f homogeneous and inhomogeneous diffusion equation is considered under the condition of onedimensional representation of the target group contingent. The examples of application of this approach are given, the results of numerical experiments are analyzed.

Results. The developed technique allows to obtain estimates of the level of information dissemination in the target group based on the use of diffusion process models.

Conclusions. The conducted experiments have confirmed the existence of sufficient adequacy of model data and data obtained as a result of real observations of the processes of change in the perception of information within specific target population groups. The prospects for further research are the development of new diffusion-type models that formalize the different nature of the influence of external factors on the processes of information dissemination. 


Keywords


Iinformation, dissemination, method of analogues, diffusion hybrid models.

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References


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GOST Style Citations


1. Smith R. Modelling Disease Ecology with Mathematics / R. Smith. – Ottawa: American Institute of Mathematical Sciences, 2017. – 291 p. ISBN-10: 1601330200,ISBN-13: 9781601330208

2. Bellman R. Mathematical methods in medicine. Singapore: World Scientific Pub. Co. Inc., 1983. – 268 p. ISBN-10: 9971950200, ISBN-13: 978-9971950200

3. Nowak A. Social Processes, Computational Models of / A. Nowak, R. R. Vallacher // Encyclopedia of Cognitive Science. – 2006. – P. 81–84. DOI: 10.1002/0470018860.s00639

4. Quastler H. The emergence of biological organization / H. Quastler. – New Haven and London: Yale University Press, 1964. – 83 p. ASIN: B0000CMHJ2

5. von Scheel H. Social Media and Business Process Management / H. von Scheel, M. Zakaria, M. von Rosing // The Complete Business Process Handbook. Body of Knowledge from Process Modeling to BPM. – 2015. – Vol. I. – P. 381–398. DOI: 10.1016/B978-0-12-799959-3.00018-5.

6. Іvohin E. V. About the use of diffusion process models for description of information extension dynamics / E. V. Ivokhin, L. Т. Аdzhubey // Scientific Bulletin of Uzhgorod University. Series of Mathematics and Informatics. – 2019. – № 1 (34). – P. 86–93. DOI: 10.24144/2616-2019.1(34).86-93.

7. Ivokhin Е. V. On Formalization of Information Dissemination Processes Based on Hybrid Diffusion Models / Е. V. Ivokhin, Yu. А. Naumenko / Journal of Automation and Information Sciences. – 2018. – Vol. 50, № 7. – P. 79–86. DOI: 10.1615/JAutomatInfScien.v50.i7.70

8. Ivokhin Е. V. On the Formalization of Dynamics in Information Processes on the Basis of Inhomogeneous One-Dimensional Diffusion Models / E. V. Ivokhin, L. Т. Аdzhubey, Е. V. Gavrylenko // Journal of Automation and Information Sciences. – 2019. – Vol.51, No. 2. – P. 22–29. DOI: 10.1615/JAutomatInfScien.v51.i2.30

9. Іvohin E. V. On the modeling of information distribution dynamics on the basis of homogeneous diffusion hybrid models/ / E. V. Ivokhin, L. Т. Аdzhubey // Scientific Bulletin of Uzhgorod University. Series of Mathematics and Informatics. – 2019. – № 2 (35). – P. 112–118. DOI: 10.24144/26167700.2019.2(35).112-118

10. Tikhonov А. N. Equations of Mathematical Physics / A. N. Tikhonov, A. A. Samarskii. – Oxford : Pergamon Press Ltd, 1963. – 776 p. ISBN-10: 0080102263, ISBN-13: 9780080102269.

11. Hairer E. Solving Ordinary Differential Equations I: Nonstiff Problems (2nd ed.) / E. Hairer, S. P. Norsett, G.Wanner. – Berlin : Springer-Verlag, 1993. – 512 p. DOI: 10.1007/978-3-54078862-1

12. Fikhtengolts G. М. Kurs differentsialnogo i integralnogo ischisleniya (in Russian). Т. 3 / G. М. Fikhtengolts. – М. : FIZMATLIT, 2008. – 728 p. ISBN-10: 5922104661 ISBN-13: 978-5922104661

13. Budak B. M. A Collection of Problems on Mathematical Physics: International Series of Monographs in Pure and Applied Mathematics/ B. M. Budak, A. A. Samarskii, A. N. Tikhonov. – Oxford : Pergamon Press Ltd, 2013. – 782 p. DOI 10.1016/C2013-0-05314-5







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