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Construction and Analysis of Nondeterministic Models of Population Dynamics

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Distributed Computer and Communication Networks (DCCN 2016)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 678))

Abstract

Three-dimensional mathematical models of population dynamics are considered in the paper. Qualitative analysis is performed for the model which takes into account the competition and diffusion of species and for the model which takes into account mutual interaction between the species. Nondeterministic models are constructed by means of transition from ordinary differential equations to differential inclusions, fuzzy and stochastic differential equations. Using the principle of reduction, which allows us to study stability properties of one type of equations, using stability properties of other types of equations, as a basis, sufficient conditions of stability are obtained. The synthesis of the corresponding stochastic models on the basis of application of the method of construction of stochastic self-consistent models is performed. The structure of these stochastic models is described and computer modelling is carried out. The obtained results are aimed at the development of methods of analysis of nondeterministic nonlinear models.

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Acknowledments

The work is partially supported by RFBR grant No. 15-07-08795.

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Authors and Affiliations

  1. Department of Applied Probability and Informatics, RUDN University (Peoples’ Friendship University of Russia), Miklukho-Maklaya Street 6, Moscow, Russia, 117198

    A. V. Demidova

  2. Federal Research Center “Computer Science and Control” of Russian Academy of Sciences, Vavilov Street 44, Building 2, Moscow, Russia, 119333

    Olga Druzhinina

  3. Department of Mathematics, University of Montenegro, Džordž Washington Street, Podgorica, Montenegro, 81000

    Milojica Jacimovic

  4. Department of Mathematical Modeling and Computer Technologies, Bunin Yelets State University, Communards Street 28, Yelets, Russia, 399770

    Olga Masina

Authors
  1. A. V. Demidova
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  2. Olga Druzhinina
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  3. Milojica Jacimovic
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  4. Olga Masina
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Corresponding author

Correspondence to A. V. Demidova .

Editor information

Editors and Affiliations

  1. V.A. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

    Vladimir M. Vishnevskiy

  2. RUDN University , Moscow, Russia

    Konstantin E. Samouylov

  3. V.A. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

    Dmitry V. Kozyrev

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Demidova, A.V., Druzhinina, O., Jacimovic, M., Masina, O. (2016). Construction and Analysis of Nondeterministic Models of Population Dynamics. In: Vishnevskiy, V., Samouylov, K., Kozyrev, D. (eds) Distributed Computer and Communication Networks. DCCN 2016. Communications in Computer and Information Science, vol 678. Springer, Cham. https://doi.org/10.1007/978-3-319-51917-3_43

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  • DOI: https://doi.org/10.1007/978-3-319-51917-3_43

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-51916-6

  • Online ISBN: 978-3-319-51917-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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