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Journal of Automation and Information Sciences
SJR: 0.232 SNIP: 0.464 CiteScore™: 0.27

ISSN Imprimer: 1064-2315
ISSN En ligne: 2163-9337

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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


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.


  1. Gubarev V.F., Daryin A.N., Lysyuchenko I.A., Nonlinear state estimator using the data on moving horizon and its application in the problem of spacecraft attitude, Mezhdunarodnyi nauchno-tekhnicheskiy zhurnal "Problemy upravleniya iinformtiki", 2011,No. 1, 118-132.

  2. Gubarev V.F., Shevchenko V.N., Gummel A.V., State estimation for systems subjected to bounded uncertainty using moving horizon approach, Prep, of the 15-th IFAC Symposium on System Identification, July 6-8, 2009, Saint-Malo, France, 2009, 910-915.

  3. Bakan G.M., Ellipsoidal algorithms for guaranteed estimating and recurrent least square method in filtration problems of dynamical systems states, Problemy upravleniya i informatiki, 1997, No. 3, 34-48.

  4. Kuntsevich V.M., Control under uncertainty conditions: guaranteed results in control and identification problems [in Russian], Naukova dumka, Kiev, 2006.

  5. Nakonechnyi O.G., Estimating parameters under uncertainty conditions, Naukovi zapysky Kyivskogo Natsionalnogo Universytetu, 2004, No. 7, 102-111.

  6. Nakonechnyi O.G., ZinkoP.M., ShevchukYu.M., Prediction estimates in mathematical models of information spread under uncertainties, Systemni doslidzhennya ta informatsiyni tekhnologii, 2017, No. 4, 54-65, DOI: 10.20535/SRIT.2308-8893.2017.4.05.

  7. Nakonechnyi A.G., Martsenyuk V.P., Controllability problems for Gompertz differential equations of dynamics, Kibernetika i sistemnyi analiz, 2004, No. 2, 123-133, DOI: 10.1023/B:CASA0000034451. 73657.88.

  8. Kalas J., Novotny J., Michalek J., Nakonechniy O., Mathematical model for cancer prevalence and cancer mortality, Taurida Journal of Computer Science Theory and Mathematics, 2013, No. 2, 44-54.

  9. Nakonechnyi O.G., Zinko P.M., Confrontation problems in systems with Gompertz dynamics, Zhurnal obchyslyuvalnoi ta prykladnoi matematyky, 2015, No. 3 (120), 50-60.

  10. Mikhailov A.P., Petrov A.P., Proncheva O.G., Marevtseva N.A., Mathematical modeling of information warfare in a society, Mediterranean Journal of Social Sciences, 2015, 6, No. 5, 27-35, DOI: 10.5901/mjss.2015.v6n5s2p27.

  11. Nakonechnyi O.G., Shevchuk Yu.M., Mathematical model of spreading information with nonstationary parameters, Visnyk KyivskogoNatsionalnogo Universytetuimeni TarasaShevchenka,. Seriya Fizyko- matematychni nauky, 2016, No. 3, 98-105.

  12. IvokhinE.V., Naumenko Yu.A, On formalization of information dissemination processes based on hybrid diffusion models, Mezhdunarodnyi nauchno-tekhnicheskiy zhurnal "Problemy upravleniya i informatiki", 2018, No. 4, 51-58, DOI: 10.1615/JAutomatInfScien.v50.i7.70.

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