Mathematical model of predator-prey interaction with accounting the areal factors and resistant factor of habitats of populations

Authors

  • Олександр Володимирович Маєвський Zhytomyr national agrarian ecology university 7 Stary Boulevard, Zhytomyr, Ukraine, 10008, Ukraine
  • Ігор Анатолійович Пількевич Zhytomyr military institute named after S. Koroliov affiliated with State university of telecommunication Mira ave., 22, Zhitomir, Ukraine, 10004, Ukraine
  • Юрій Борисович Бродський Zhytomyr national agrarian ecology university 7 Stary Boulevard, Zhytomyr, Ukraine, 10008, Ukraine

DOI:

https://doi.org/10.15587/2313-8416.2015.40445

Keywords:

generalized mathematical model, random walk, diffusion processes, Markov chain, resistance of habitat

Abstract

The article gives coverage to refinement upon the mathematical model of predator-prey interaction taking into account the areal factors and resistant factor of habitats of populations. It is grounded the physical interpretation of proposed mathematical model and its connection with diffusion process, which could be described with the Ehrenfests diffusion model that lead to formation of Markov chain.. For further use of proposed mathematical model of population dynamics, it is made its identification and the estimation of adequacy by comparing the relative error of simulation results

Author Biographies

Олександр Володимирович Маєвський, Zhytomyr national agrarian ecology university 7 Stary Boulevard, Zhytomyr, Ukraine, 10008

Postgraduate student

Department of environmental monitoring

Ігор Анатолійович Пількевич, Zhytomyr military institute named after S. Koroliov affiliated with State university of telecommunication Mira ave., 22, Zhitomir, Ukraine, 10004

Doctor of Engineering, Professor

Department of computer systems

Юрій Борисович Бродський, Zhytomyr national agrarian ecology university 7 Stary Boulevard, Zhytomyr, Ukraine, 10008

Doctor of Philosophy

Department of information technologies and system modelling

References

Bogoboâŝij, V. V., Čurbanov, K. R., Monger, P. R., Šmandìj, V. M. (2004). Principles of modeling and forecasting in Ecology: tutorial. Center for educational l-RI, 216.

Rizničenko, G. Y., Rubin, A. B. (1993). Mathematical models of biological productive processes: Teaching aid. Moscow: Ed-vo MGU, 302.

Rafe, F. (1977). Statistical physics. N.: Science, 311.

Ehrenfest, P., Ehrenfest, T. (1907). Über zwei bekannte Einwände gegen das Boltzmannsche H-Theorem, Physikalishe zeitchrift, 8, 311–314.

Manturov, O. (1991). Higher mathematics course. Moscow.: "Vysšaâ schkola", 251.

Dobrovolsky, V. (2005). Basical theory of ecological systems. Kiev: PUBLISHING HOUSE «Pro», 272.

Timonìn, Y. O., Brodsky, Y. B., Grabar, I. G. (2009). Universal model of systems: methodological aspect. Vis. ŽNAEU: of Sciences.-teoret. UK, 1, 358–366.

Timonìn, Y. O. (1999). Conceptual basis of business engineering. Economics and management, 1 (2), 74–79.

Timonìn, Y. O. (1999). Principles of energy interactions of systems. Visn. ZITI, 9, 150–155.

Modeling and forecasting the dynamics of artiodactyl in hunting farms of radioactively contaminated territory of Zhytomyr region: report of the GDR (2011). ZNAEU, Min. Agrarian policy of Ukraine; Sciences. Coeur. and a. Pilkevich. DR № 0111U009694. Zhytomyr, 84.

Majewski, O. V., Pilkevich, I. A., Kotkov, V. I. (2012). Substantiation of generalized logistic model of dynamics of populations. Eastern-European Journal Of Enterprise Technologies, 1/4 (55), 63–66. Available at: http://journals.uran.ua/eejet/article/view/3325/3125

Guidelines on the arrangement of hunting grounds (2002). Kiev: Publishing House of Deržkomlìsu Ukraine, 113.

Feller, V. (1984). Introduction to probability theory and its application. Vol. 1. Moscow: Mir, 527.

Kolmogorov, A. N., Petrovskij, N. G., Piskunov, N. S. (1937). Study of diffusion equation, connected with the increase of substance and its application to a biological problem. Newsletter. The moscow state university. Ser. A. mathematics and mechanics, 1 (6), 1–16.

Vandermeer, J. (1982). On the resolution of chaos in population models. Theoretical population biology, 22 (1), 17–27. doi: 10.1016/0040-5809(82)90033-8

Downloads

Published

2015-04-27

Issue

Vol. 4 No. 2 (9) (2015)

Section

Technical Sciences

License

Copyright (c) 2015 Александр Владимирович Маевский, Ігор Анатолійович Пількевич, Юрій Борисович Бродський

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Our journal abides by the Creative Commons CC BY copyright rights and permissions for open access journals.

Authors, who are published in this journal, agree to the following conditions:

1. The authors reserve the right to authorship of the work and pass the first publication right of this work to the journal under the terms of a Creative Commons CC BY, which allows others to freely distribute the published research with the obligatory reference to the authors of the original work and the first publication of the work in this journal.

 2. The authors have the right to conclude separate supplement agreements that relate to non-exclusive work distribution in the form in which it has been published by the journal (for example, to upload the work to the online storage of the journal or publish it as part of a monograph), provided that the reference to the first publication of the work in this journal is included.