ГАРАНТОВАНІ ПРОГНОЗНІ ОЦІНКИ РОЗВʼЯЗКІВ СИСТЕМ ДИФЕРЕНЦІАЛЬНИХ РІВНЯНЬ З ДИНАМІКОЮ ГОМПЕРЦА ПРИ СПОСТЕРЕЖЕННЯХ У ДИСКРЕТНІ МОМЕНТИ ЧАСУ

• Datum: 2025
• Hauptverfasser: Nakonechnyi, A.G., Zinko, P.N., Zinko, T.P., Shevchuk, Yu.M.
• Format: Artikel
• Sprache: English
• Veröffentlicht: V.M. Glushkov Institute of Cybernetics of NAS of Ukraine 2025
• Schlagworte: системи нелінійних диференціальних рівнянь; динаміка Гомперца; прогнозні гарантовані оцінки; дискретні спостереження; невизначеність
• Online Zugang: https://jais.net.ua/index.php/files/article/view/654
• Назва журналу: Problems of Control and Informatics

In this paper, we introduce a mathematical model of spreading information messages. Suppose, a community is influenced by one of n sources of information. The number of information made by each of the sides is taken as key parameter promoting accomplishment of aim. Information can be spread in the community along internal (interpersonal communication of the member of social community) and external information flow. The model has the form of a system of non-linear differential equations with Gompertzian dynamics and non-stationary parameters. These mathematical models can be useful for describe processes that grow rapidly over time. Systems of differential equations with Gompertzian dynamics claim to be an adequate representation of processes from the subject area because they have a non-linear right part. The problem of finding predictive an estimate of the dynamics of such processes is practically an important problem of analyzing the information spreading process in society. This problem becomes nontrivial for the systems of differential equations with Gompertz because there are natural logarithms in the right sides of these equations. We formulated the problem of finding the predictive estimation and error for the systems of differential equations with Gompertzian dynamics. We the algorithms for building guaranteed predictive estimations and error and approximate guaranteed predictive estimations offered for the special case of this problem with discrete observations. We consider the results of problem numerical experiments to build guaranteed estimates for mathematical model of spreading one type of information. The analysis of these results has demonstrated the practical meaning of the obtained approach. The obtained results can be useful for the development of decision support systems for analyzing processes in the socio-communicative space.