Design and computer research of a nonlinear stochastic models describing the dynamics of interacting populations

The construction of nonlinear three-dimensional models of interconnected communities number dynamics is considered, taking into account competition in populations of victims. A qualitative research of the systems is carried out, equilibrium states are found, the species number dynamics graphs are constructed. For these models, an estimate of the model parameters is given and local phase portraits are constructed. The transition to the corresponding stochastic models is made. In stochastic cases, the method of constructing self-consistent stochastic models is used. A comparative analysis of deterministic and stochastic models is carried out. Effects typical for three-dimensional models with regard to competition in prey populations are revealed. A software package for the numerical solution of differential equations systems by modified Runge-Kutta methods is used as a software tool for researching the model. The software package allows performing numerical experiments based on the implementation of algorithms for generating trajectories of multidimensional Wiener processes and multipoint distributions and algorithms for solving stochastic differential equations. The formulation of the optimal control problem is proposed. Computer research of the models makes it possible to obtain the results of numerical experiments on the search for trajectories and the estimation of parameters. The results obtained can find application in problems of ecological systems computer modeling, as well as in problems of synthesis, optimal control and analysis of the multidimensional stochastic models stability describing the dynamics of interacting populations. © 2021 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).

Demidova A.V. 1 , Druzhinina O.V. 2 , Masina O.N. 3 , Shcherbakov A.V.3
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  • 1 Peoples' Friendship University of Russia, Rudn University, 6, Miklukho-Maklaya St., Moscow, 117198, Russian Federation
  • 2 Federal Research Center, Computer Science and Control of Russian Academy of Sciences, 44, building 2, Vavilov St., Moscow, 119333, Russian Federation
  • 3 Bunin Yelets State University, 28, Kommunarov St., Yelets, 399770, Russian Federation
Computer modeling; Nonlinear model of population dynamics; Optimal control; Software package; Stochastization of one-step processes; Symbolic computation libraries
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