Mathematical modeling of the delay process in regulation of population dynamics based on the theory of cellular automation
https://doi.org/10.23947/2587-8999-2019-1-1-35-49
Abstract
The paper covers the research and parameterization of the delay effect in regulation of biological kinetics processes for interacting populations, including the modification of the mathematical model to describe the development of population fluctuations. Numerical implementation of the modified Conway algorithm for a cellular automaton with a ternary state of cells was developed for analysis the model scenarios of dynamics of nonlinear interacting biological populations, taking into account factors that have a significant influence on the nature of researched processes. The transformation conditions of the cells’ state show that the formalized delay can refer to the dynamics of interaction of species and supporting the living conditions of the environment. A numerical implementation of a fundamentally different version of the cellular automaton was proposed. The cellular automaton allow modeling the processes of population dynamics regulation taking into account the delay effect on the basis of three dynamically interacting factors: ontogenetic delay, the necessary to restore resources, and diffusion component depending on the development rate of individuals in the population.
Keywords
Supporting agencies: The paper was supported with the financial support by the grant № 17-11-01286 of the Russian Science Foundation
About the Authors
Alla Valeryevna Nikitina
Southern Federal University
(Chekhov str., 2, Taganrog, Russian Federation)
Russian Federation
Russian Federation
Nikitina Alla Valeryevna, Southern Federal University (Chekhov str., 2, Taganrog, Russian Federation), Doctor of Technical Science, Associate professor
V. M. Kozlov
Russian Federation
Alena Aleksandrovna Filina
Supercomputers and Neurocomputers Research Center, Co Ltd.
(Italyansky lane, 106, Taganrog, Russian Federation)
Russian Federation
Russian Federation
Filina Alena Aleksandrovna, Supercomputers and Neurocomputers Research Center, Co Ltd. (Italyansky lane, 106, Taganrog, Russian Federation), Candidate of Technical Science, Researcher
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Review
For citations:
Nikitina A.V., Kozlov V.M., Filina A.A. Mathematical modeling of the delay process in regulation of population dynamics based on the theory of cellular automation. Computational Mathematics and Information Technologies. 2019;3(1). (In Russ.) https://doi.org/10.23947/2587-8999-2019-1-1-35-49
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