Construction and analysis of nondeterministic models of population dynamics

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. © Springer International Publishing AG 2016.

Авторы
Demidova A.V. 1 , Druzhinina O.2 , Jacimovic M.3 , Masina O.4
Издательство
Springer Verlag
Язык
Английский
Страницы
498-510
Статус
Опубликовано
Том
678
Год
2016
Организации
  • 1 Department of Applied Probability and Informatics, RUDN University (Peoples’ Friendship University of Russia), Miklukho-Maklaya Street 6, Moscow, 117198, Russian Federation
  • 2 Federal Research Center “Computer Science and Control” of Russian Academy of Sciences, Vavilov Street 44, Building 2, Moscow, 119333, Russian Federation
  • 3 Department of Mathematics, University of Montenegro, Džordž Washington Street, Podgorica, 81000, Montenegro
  • 4 Department of Mathematical Modeling and Computer Technologies, Bunin Yelets State University, Communards Street 28, Yelets, 399770, Russian Federation
Ключевые слова
Computer modelling; Differential equations; Population dynamics; Principle of a reduction; Single-step processes; Stability; Stochastic model
Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/4254/