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Портал Begell Электронная Бибилиотека e-Книги Журналы Справочники и Сборники статей Коллекции
Journal of Automation and Information Sciences
SJR: 0.232 SNIP: 0.464 CiteScore™: 0.27

ISSN Печать: 1064-2315
ISSN Онлайн: 2163-9337

Выпуски:
Том 51, 2019 Том 50, 2018 Том 49, 2017 Том 48, 2016 Том 47, 2015 Том 46, 2014 Том 45, 2013 Том 44, 2012 Том 43, 2011 Том 42, 2010 Том 41, 2009 Том 40, 2008 Том 39, 2007 Том 38, 2006 Том 37, 2005 Том 36, 2004 Том 35, 2003 Том 34, 2002 Том 33, 2001 Том 32, 2000 Том 31, 1999 Том 30, 1998 Том 29, 1997 Том 28, 1996

Journal of Automation and Information Sciences

DOI: 10.1615/JAutomatInfScien.v51.i5.40
pages 38-53

Guaranteed Prediction Estimates of Solving Systems of Differential Equations with Gompertz Dynamics under Observations at Discrete Time Instants

Alexander G. Nakonechnyi
Kiev National Taras Shevchenko University, Kiev
Petr N. Zinko
Kiev National Taras Shevchenko University, Kiev
Taras P. Zinko
Kiev National Taras Shevchenko University, Kiev
Yulia M. Shevchuk
Kiev National Taras Shevchenko University, Kiev

Краткое описание

The mathematical model of information spread in a social medium is analyzed. It is assumed that in a sociocommunicative space there spread n types of information messages different in content. The number of individuals spreading one of the types of information messages is a key indicator of the model dynamics. Information messages spread through internal (interpersonal communication) and external (media influence) flows. The model is presented in the form of the system of n Gompertz nonlinear differential equations. It is appropriate to apply such models in practical problems of analyzing an information spread in a social medium dynamics of which is fast growing in time. Having a nonlinear right part such models claim to be an adequate representation of processes in a subject area. One of the practical important problems which occur while analyzing processes of information spread in a social medium is the problem of finding prediction estimates of such processes dynamics. For the systems of Gompertz differential equations this problem becomes nontrivial due to natural logarithms in the right-hand sides of these equations. The problem of finding the guaranteed prediction estimates of vectors is formulated. For a particular case of this problem with discrete observations there were proposed the efficient algorithms for finding guaranteed and approximate guaranteed prediction estimates of state and error vectors of prediction guaranteed estimates. As example there are presented results of finding the guaranteed prediction estimates of dynamics of mathematical model of one form information spread in a social medium. Results of numerical computer experiment demonstrate practical opportunities of this scheme. The proposed technique can be used for development of decision support systems for analyzing processes in sociocommunicative space.

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