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

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

MMC.
2019;
Volume 6, Number 1
: pp. 92-100
https://doi.org/10.23939/mmc2019.01.092
Received: March 20, 2019
Accepted: May 02, 2019

Math. Model. Comput. Vol.6, No.1, pp.92-100 (2019)

Authors:
  1. O. Nakonechnyi
  2. P. Zinko
  3. I. Shevchuk
1
Taras Shevchenko National University of Kyiv
2
Taras Shevchenko National University of Kyiv
3
Taras Shevchenko National University of Kyiv

In 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.

system of differential non-linear equations
Gompertzian dynamics
guaranteed predictive estimation
uncertainty
  1. Kalas J., Novotny J., Michalek J., Nakonechnyi O. G.  Mathematical model for cancer prevalence and cancer mortality.  Taurida Journal of Computer Science Theory and Mathematics. 2, 44--54 (2013).
  2. Nakonechnyi O. G., Zinko P. M.  Confrontation problems with the dynamics Gompertzian systems.  Journal of Computational and Applied Mathematics. 3 (120), 50--60 (2015), (in Ukrainian).
  3. Nakonechnyi O. G.  Parameters estimation under uncertainty.  Scientific notes of National University of Kyiv, Faculty of Cybernetics. VII, 102--111 (2004), (in Ukrainian).
  4. Nakonechnyi O. 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).
  5. Nakonechnyi O. 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).
  6. Nakonechnyi O. G., Shevchuk I. M., Chicrii V. K.  Estimation of non-stationary parameters of differential equations under uncertainty.  Cybernetics and system analysis. 4,  109--121 (2018), (in Ukrainian).
  7. Nakonechnyi O. 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).
  8. Nakonechnyi O. 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).
  9. Bublik B. N., Danilov V. Y., Nakonechnyi O. G.  Some observation and control problems in linear systems.  Kyiv, UMK VO (1988), (in Russian).               
  10. Mikhailov A. P., Marevtseva N. A.  Models of Information Warfare.  Mathematical Models and Computer Simulations. 4 (3), 251--259 (2012).
  11. Mishra B. K., Prajapati A.  Modelling and simulation: cyber war.  Procedia Technology. 10, 987--997 (2013).
  12. Kereselidze N. 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).
  13. Nakonechnyi O. G., Shevchuk I. M.  Mathematical model of information spreading process with non-stationary parameters.  Bulletin of Taras Shevchenko National University of Kiev. Series Physics and Mathematics. 3, 98--105 (2016), (in Ukrainian).
  14. Ivokhin E. 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).