Guaranteed predictive estimation of solutions of system of differential equations with the Gompertzian dynamics

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dc.citation.epage100
dc.citation.issue1
dc.citation.spage92
dc.contributor.affiliationКиївський національний університет імені Тараса Шевченка
dc.contributor.affiliationTaras Shevchenko National University of Kyiv
dc.contributor.authorНаконечний, О.
dc.contributor.authorЗінько, П.
dc.contributor.authorШевчук, Ю.
dc.contributor.authorNakonechnyi, O.
dc.contributor.authorZinko, P.
dc.contributor.authorShevchuk, I.
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.date.accessioned2020-02-27T09:45:15Z
dc.date.available2020-02-27T09:45:15Z
dc.date.created2019-02-26
dc.date.issued2019-02-26
dc.description.abstractУ роботі досліджено математичну модель у формі системи нелінійних диференціальних рівнянь із динамікою Гомперца, яка може бути застосована для моделювання процесів, що швидко зростають за часом. Сформульовано та розв’язано задачу знаходження гарантованих прогнозних оцінок для систем диференціальних рівнянь з динамікою Гомперца для випадку неперервних спостережень. Як приклади подано результати визначення гарантованих прогнозних оцінок динаміки математичної моделі поширення одного виду інформації в соціумі.
dc.description.abstractIn this paper, we have introduced a mathematical model to describe processes that grow in time rapidly. The model has the form of a system of non-linear differential equations with Gompertzian dynamics and non-stationary parameters. We have formulated and studied the problem of finding the predictive estimation for the systems of differential equations with Gompertzian dynamics, for the case of continuous observation. We have suggested the algorithms for building guaranteed predictive estimations for the model. We have presented as an example, the results of numerical experiments to build guaranteed estimates for the mathematical model of spreading some type of information in society. The suggested approach presents both theoretical interest and important practical meaning.
dc.format.extent92-100
dc.format.pages9
dc.identifier.citationNakonechnyi O. Guaranteed predictive estimation of solutions of system of differential equations with the Gompertzian dynamics / O. Nakonechnyi, P. Zinko, I. Shevchuk // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2019. — Vol 6. — No 1. — P. 92–100.
dc.identifier.citationenNakonechnyi O. Guaranteed predictive estimation of solutions of system of differential equations with the Gompertzian dynamics / O. Nakonechnyi, P. Zinko, I. Shevchuk // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2019. — Vol 6. — No 1. — P. 92–100.
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/46144
dc.language.isoen
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofMathematical Modeling and Computing, 1 (6), 2019
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dc.relation.references2. NakonechnyiO.G., Zinko P.M. Confrontation problems with the dynamics Gompertzian systems. Journal of Computational and Applied Mathematics. 3 (120), 50–60 (2015), (in Ukrainian).
dc.relation.references3. NakonechnyiO.G. Parameters estimation under uncertainty. Scientific notes of National University of Kyiv, Faculty of Cybernetics. VII, 102–111 (2004), (in Ukrainian).
dc.relation.references4. NakonechnyiO.G. Problem of guaranteed estimation of parameters in dynamics. Abstracts XVII International Conference “Problem of decision making under uncertainties”. Shidnycya, Ukraine. May 23–27. P. 141 (2011), (in Ukrainian).
dc.relation.references5. NakonechnyiO.G., Zinko P.M., Shevchuk I.M. Predictive estimation of mathematical models of information spreading process under uncertainty. System Research and Information Technologies. 4, 54–65 (2017), (in Ukrainian).
dc.relation.references6. NakonechnyiO.G., Shevchuk I.M., ChicriiV.K. Estimation of non-stationary parameters of differential equations under uncertainty. Cybernetics and system analysis. 4, 109–121 (2018), (in Ukrainian).
dc.relation.references7. NakonechnyiO.G., Zinko P.M., Shevchuk I.M. Guaranteed estimation of non-stationary parameters of difference equations under uncertainty. Journal of Automation and Information Sciences. 6, 41–54 (2018), (in Russian).
dc.relation.references8. NakonechnyiO.G. Problem of guaranteed estimation of parameters in dynamics. Abstracts XXXIII International Conference “Problem of decision making under uncertainties”. Hurgada, Egypt. Jauare 24 – February 1. P. 64–66 (2019).
dc.relation.references9. BublikB.N., DanilovV.Y., NakonechnyiO.G. Some observation and control problems in linear systems. Kyiv, UMK VO (1988), (in Russian).
dc.relation.references10. MikhailovA.P., MarevtsevaN.A. Models of Information Warfare. Mathematical Models and Computer Simulations. 4 (3), 251–259 (2012).
dc.relation.references11. MishraB.K., PrajapatiA. Modelling and simulation: cyber war. Procedia Technology. 10, 987–997 (2013).
dc.relation.references12. KereselidzeN.G. An optimal control problem in mathematical and computer models of the information warfare. Differential and Difference Equations with Applications: ICDDEA, Amadora, Portugal, May 2015, Selected Contributions. Springer Proceedings in Mathematics and Statistics, 164. Springer International Publishing Switzerland. P. 303–311 (2015).
dc.relation.references13. NakonechnyiO.G., Shevchuk I.M. Mathematical model of information spreading process with nonstationary parameters. Bulletin of Taras Shevchenko National University of Kiev. Series Physics and Mathematics. 3, 98–105 (2016), (in Ukrainian).
dc.relation.references14. IvokhinE.V., Adzhubey L.T., Gavrylenko E.V. Guaranteed estimation of non-stationary parameters of difference equations under uncertainty. Journal of Automation and Information Sciences. 1, 5–12 (2019), (in Russian).
dc.relation.referencesen1. Kalas J., Novotny J., Michalek J., NakonechnyiO.G. Mathematical model for cancer prevalence and cancer mortality. Taurida Journal of Computer Science Theory and Mathematics. 2, 44–54 (2013).
dc.relation.referencesen2. NakonechnyiO.G., Zinko P.M. Confrontation problems with the dynamics Gompertzian systems. Journal of Computational and Applied Mathematics. 3 (120), 50–60 (2015), (in Ukrainian).
dc.relation.referencesen3. NakonechnyiO.G. Parameters estimation under uncertainty. Scientific notes of National University of Kyiv, Faculty of Cybernetics. VII, 102–111 (2004), (in Ukrainian).
dc.relation.referencesen4. NakonechnyiO.G. Problem of guaranteed estimation of parameters in dynamics. Abstracts XVII International Conference "Problem of decision making under uncertainties". Shidnycya, Ukraine. May 23–27. P. 141 (2011), (in Ukrainian).
dc.relation.referencesen5. NakonechnyiO.G., Zinko P.M., Shevchuk I.M. Predictive estimation of mathematical models of information spreading process under uncertainty. System Research and Information Technologies. 4, 54–65 (2017), (in Ukrainian).
dc.relation.referencesen6. NakonechnyiO.G., Shevchuk I.M., ChicriiV.K. Estimation of non-stationary parameters of differential equations under uncertainty. Cybernetics and system analysis. 4, 109–121 (2018), (in Ukrainian).
dc.relation.referencesen7. NakonechnyiO.G., Zinko P.M., Shevchuk I.M. Guaranteed estimation of non-stationary parameters of difference equations under uncertainty. Journal of Automation and Information Sciences. 6, 41–54 (2018), (in Russian).
dc.relation.referencesen8. NakonechnyiO.G. Problem of guaranteed estimation of parameters in dynamics. Abstracts XXXIII International Conference "Problem of decision making under uncertainties". Hurgada, Egypt. Jauare 24 – February 1. P. 64–66 (2019).
dc.relation.referencesen9. BublikB.N., DanilovV.Y., NakonechnyiO.G. Some observation and control problems in linear systems. Kyiv, UMK VO (1988), (in Russian).
dc.relation.referencesen10. MikhailovA.P., MarevtsevaN.A. Models of Information Warfare. Mathematical Models and Computer Simulations. 4 (3), 251–259 (2012).
dc.relation.referencesen11. MishraB.K., PrajapatiA. Modelling and simulation: cyber war. Procedia Technology. 10, 987–997 (2013).
dc.relation.referencesen12. KereselidzeN.G. An optimal control problem in mathematical and computer models of the information warfare. Differential and Difference Equations with Applications: ICDDEA, Amadora, Portugal, May 2015, Selected Contributions. Springer Proceedings in Mathematics and Statistics, 164. Springer International Publishing Switzerland. P. 303–311 (2015).
dc.relation.referencesen13. NakonechnyiO.G., Shevchuk I.M. Mathematical model of information spreading process with nonstationary parameters. Bulletin of Taras Shevchenko National University of Kiev. Series Physics and Mathematics. 3, 98–105 (2016), (in Ukrainian).
dc.relation.referencesen14. IvokhinE.V., Adzhubey L.T., Gavrylenko E.V. Guaranteed estimation of non-stationary parameters of difference equations under uncertainty. Journal of Automation and Information Sciences. 1, 5–12 (2019), (in Russian).
dc.rights.holderCMM IAPMM NAS
dc.rights.holder© 2019 Lviv Polytechnic National University
dc.subjectсистеми нелінійних диференціальних рівнянь
dc.subjectдинаміка Гомперца
dc.subjectпрогнозні гарантовані оцінки
dc.subjectневизначеність
dc.subjectsystem of differential non-linear equations
dc.subjectGompertzian dynamics
dc.subjectguaranteed predictive estimation
dc.subjectuncertainty
dc.subject.udc517.9
dc.subject.udc519.87
dc.titleGuaranteed predictive estimation of solutions of system of differential equations with the Gompertzian dynamics
dc.title.alternativeГарантовані прогнозні оцінки розв‘язків систем диференціальних рівнянь із динамікою Гомперца
dc.typeArticle

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Mathematical Modeling And Computing. – 2019. – Vol. 6, No. 1