https://oldena.lpnu.ua/handle/ntb/44890| Title: | Stability under stochastic perturbation of solutions of mathematical models of information spreading process with external control |
| Other Titles: | Стійкість під час стохастичних збурень розв’язків у математичних моделях розповсюдження інформації зі зовнішніми впливами |
| Authors: | Наконечний, О. Шевчук, Ю. Nakonechnyi, O. Shevchuk, I. |
| Affiliation: | Київський національний університет імені Тараса Шевченка Taras Shevchenko National University of Kyiv |
| Bibliographic description (Ukraine): | Nakonechnyi O. Stability under stochastic perturbation of solutions of mathematical models of information spreading process with external control / O. Nakonechnyi, I. Shevchuk // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2018. — Vol 5. — No 1. — P. 66–73. |
| Bibliographic description (International): | Nakonechnyi O. Stability under stochastic perturbation of solutions of mathematical models of information spreading process with external control / O. Nakonechnyi, I. Shevchuk // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2018. — Vol 5. — No 1. — P. 66–73. |
| Is part of: | Mathematical Modeling and Computing, 1 (5), 2018 |
| Journal/Collection: | Mathematical Modeling and Computing |
| Issue: | 1 |
| Volume: | 5 |
| Issue Date: | 15-Jan-2018 |
| Publisher: | Lviv Politechnic Publishing House |
| Place of the edition/event: | Lviv |
| UDC: | 517.9 |
| Keywords: | математична модель поширення інформації стохастична стійкість асимптотична стійкість у середньоквадратичному “білий” шум mathematical model of information spreading process stochastic stability asymptotic stability in quadratic average “white” noise |
| Number of pages: | 8 |
| Page range: | 66-73 |
| Start page: | 66 |
| End page: | 73 |
| Abstract: | Наведено загальну схему аналізу стохастичної стiйкості за першим наближенням в
околi точок стiйкості моделі розповсюдження довільної кількості типів iнформацiї на
прикладах узагальненої моделі з стацiонарними параметрами та моделi з нестаціонар-
ними параметрами та спецiальним представленням зовнiшнього впливу. Результати
числового експерименту демонструють практичнi можливостi цiєї схеми. Отриманi
результати дали змогу визначати для параметрiв моделi допустимi областi, значен-
ня з яких будуть гарантувати асимптотичну стiйкiсть у середньоквадратичному за
першим наближенням в околi стацiонарних точок. In this paper mathematical model of spreading any number of information types with external influences is considered. The model takes the form of n (number of information channels) non-linear Ito stochastic differential equations. Conditions for asymptotic stability in quadratic average in first-approximation of the special points are considered for general stationary model and special case with non-stationary parameters. The results of example are presented for the special case of the base model with stationary parameters. |
| URI: | https://ena.lpnu.ua/handle/ntb/44890 |
| Copyright owner: | © 2018 Lviv Polytechnic National University CMM IAPMM NASU © 2018 Lviv Polytechnic National University CMM IAPMM NASU |
| References (Ukraine): | [1] MikhailovA.P., MarevtsevaN.A. Models of Information Warfare. Mathematical Models and Computer Simulations. 3 (4), 251–259 (2012). [2] MikhailovA.P., PetrovA.P., PronchevaO.G., MarevtsevaN.A. Mathematical Modeling of Information Warfare in a Society. Mediterranean Journal of Social Sciences. 6 (5), 27–35 (2015). [3] 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). [4] 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). [5] Shevchuk I.M. Stability of solutions of mathematical models of information spreading process with external control. Journal of Computational and Applied Mathematics. 1 (124), 99–111 (2017), (in Ukrainian). [6] NakonechnyiO.G. Best-mean estimates in models of information confrontation. Abstracts XXIV International Conference “Problem of decision making under uncertainties”. Cesky Rudolec, Czech Republic. September 1 5. P. 114–115 (2014). [7] NakonechnyiO.G., Zinko P.M. Estimates of unsteady parameters in model of information confrontation. Abstracts XXVIII International Conference “Problem of decision making under uncertainties”. Brno, Czech Republic. August 25–30. P. 82–83 (2016). [8] NakonechnyiO.G., Zinko P.M., Shevchuk I.M. Averaged optimal predictive estimation of mathematical models of information spreading process under uncertainty. Bulletin of Taras Shevchenko National University of Kiev. Series Physics and Mathematics. 2, 122–127 (2017). [9] 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). [10] NakonechnyiO.G., Zinko P.M., Shevchuk I.M. Analysis of non-stationary mathematical models of information spreading process under uncertainty. Abstracts of International Scientific Conference “Modern Problems of Mathematical Modeling, Computational Mathematical Methods and Information Technologies”. Rivne, Ukraine. P. 108–110 (2018), (in Ukrainian). [11] DemidovichB.P. Lectures on the mathematical theory of stability. Moscow, Nauka (1967), (in Russian). |
| References (International): | [1] MikhailovA.P., MarevtsevaN.A. Models of Information Warfare. Mathematical Models and Computer Simulations. 3 (4), 251–259 (2012). [2] MikhailovA.P., PetrovA.P., PronchevaO.G., MarevtsevaN.A. Mathematical Modeling of Information Warfare in a Society. Mediterranean Journal of Social Sciences. 6 (5), 27–35 (2015). [3] 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). [4] 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). [5] Shevchuk I.M. Stability of solutions of mathematical models of information spreading process with external control. Journal of Computational and Applied Mathematics. 1 (124), 99–111 (2017), (in Ukrainian). [6] NakonechnyiO.G. Best-mean estimates in models of information confrontation. Abstracts XXIV International Conference "Problem of decision making under uncertainties". Cesky Rudolec, Czech Republic. September 1 5. P. 114–115 (2014). [7] NakonechnyiO.G., Zinko P.M. Estimates of unsteady parameters in model of information confrontation. Abstracts XXVIII International Conference "Problem of decision making under uncertainties". Brno, Czech Republic. August 25–30. P. 82–83 (2016). [8] NakonechnyiO.G., Zinko P.M., Shevchuk I.M. Averaged optimal predictive estimation of mathematical models of information spreading process under uncertainty. Bulletin of Taras Shevchenko National University of Kiev. Series Physics and Mathematics. 2, 122–127 (2017). [9] 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). [10] NakonechnyiO.G., Zinko P.M., Shevchuk I.M. Analysis of non-stationary mathematical models of information spreading process under uncertainty. Abstracts of International Scientific Conference "Modern Problems of Mathematical Modeling, Computational Mathematical Methods and Information Technologies". Rivne, Ukraine. P. 108–110 (2018), (in Ukrainian). [11] DemidovichB.P. Lectures on the mathematical theory of stability. Moscow, Nauka (1967), (in Russian). |
| Content type: | Article |
| Appears in Collections: | Mathematical Modeling And Computing. – 2018. – Vol. 5, No. 1 |
| File | Description | Size | Format | |
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| 2018v5n1_Nakonechnyi_O-Stability_under_stochastic_66-73.pdf | 847.47 kB | Adobe PDF | View/Open | |
| 2018v5n1_Nakonechnyi_O-Stability_under_stochastic_66-73__COVER.png | 361.38 kB | image/png | View/Open |
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