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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2024, Volume 64, Number 8, Pages 1409–1423
DOI: https://doi.org/10.31857/S0044466924080067 (Mi zvmmf11809) 		 
General numerical methods

Estimates for solutions of a biological model with infinite distributed delay

T. K. Iskakovab, M. A. Skvortsovaab

a Novosibirsk State University, 630090, Novosibirsk, Russia
b Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, 630090, Novosibirsk, Russia
DOI: https://doi.org/10.31857/S0044466924080067
Abstract: For several species of microorganisms, a competition model described by a system of nonlinear differential equations with an infinite distributed delay is considered. The asymptotic stability of the equilibrium point corresponding to the survival of only one species and extinction of the others is studied. Conditions on the initial species population sizes and the initial nutrient concentration are indicated under which the system reaches the equilibrium. Additionally, the stabilization rate is estimated. The results are obtained using a Lyapunov–Krasovskii functional.
Key words: species competition model, chemostat, delay differential equations, infinite distributed delay, equilibrium point, asymptotic stability, estimates for solutions, domain of attraction, Lyapunov–Krasovskii functional.
Funding agency Grant number
Mathematical Center in Akademgorodok 075-15-2022-282
This work was supported by the Mathematical Center in Akademgorodok under agreement no. 075-15-2022-282 with the Ministry of Science and Higher Education of the Russian Federation.
Received: 02.04.2024
Revised: 02.04.2024
Accepted: 02.05.2024
English version:
Computational Mathematics and Mathematical Physics, 2024, Volume 64, Issue 8, Pages 1689–1703
DOI: https://doi.org/10.1134/S0965542524700921
Bibliographic databases:
Document Type: Article
UDC: 517.929.4
Language: Russian
Citation: T. K. Iskakov, M. A. Skvortsova, “Estimates for solutions of a biological model with infinite distributed delay”, Zh. Vychisl. Mat. Mat. Fiz., 64:8 (2024), 1409–1423; Comput. Math. Math. Phys., 64:8 (2024), 1689–1703
Citation in format AMSBIB
\Bibitem{IskSkv24}
\by T.~K.~Iskakov, M.~A.~Skvortsova
\paper Estimates for solutions of a biological model with infinite distributed delay
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2024
\vol 64
\issue 8
\pages 1409--1423
\mathnet{http://mi.mathnet.ru/zvmmf11809}
\crossref{https://doi.org/10.31857/S0044466924080067}
\elib{https://elibrary.ru/item.asp?id=75224104}
\transl
\jour Comput. Math. Math. Phys.
\yr 2024
\vol 64
\issue 8
\pages 1689--1703
\crossref{https://doi.org/10.1134/S0965542524700921}
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