Estimates of solutions to differential equations with distributed delay describing the competition of several types of microorganisms Full article
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Journal of Applied and Industrial Mathematics
ISSN: 1990-4789 , E-ISSN: 1990-4797 |
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| Output data | Year: 2022, Volume: 16, Number: 4, Pages: 800-808 Pages count : 9 DOI: 10.1134/S1990478922040196 | ||
| Tags | species competition model, chemostat, delay differential equation, infinite distributed delay, solution estimate, Lyapunov–Krasovskii functional | ||
| Authors |
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| Affiliations |
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Funding (1)
| 1 |
Министерство науки и высшего образования РФ Mathematical Center in Akademgorodok |
075-15-2019-1613, 075-15-2022-281 |
Abstract:
We consider a model of n-species competition in a chemostat. This model is a system of n+1 differential equations with infinite distributed delay. The system consists of one equation for the nutrient concentration dynamics and n equations for the species population dynamics. The transformation of the nutrient into viable cells does not occur instantly and requires some time, which is taken into account by the presence of a delay. Under the condition that the concentration of the input nutrient is below a certain level, Lyapunov–Krasovskii functionals are constructed with the help of which estimates are obtained for all components of the solutions. The estimates characterize the extinction rates of all species in the chemostat and the rate of stabilization of the nutrient concentration to a constant concentration value.
Cite:
Skvortsova M.A.
, Yskak T.
Estimates of solutions to differential equations with distributed delay describing the competition of several types of microorganisms
Journal of Applied and Industrial Mathematics. 2022. V.16. N4. P.800-808. DOI: 10.1134/S1990478922040196 Scopus РИНЦ OpenAlex
Estimates of solutions to differential equations with distributed delay describing the competition of several types of microorganisms
Journal of Applied and Industrial Mathematics. 2022. V.16. N4. P.800-808. DOI: 10.1134/S1990478922040196 Scopus РИНЦ OpenAlex
Original:
Скворцова М.А.
, Искаков Т.К.
Оценки решений дифференциальных уравнений с распределенным запаздыванием, описывающих конкуренцию нескольких видов микроорганизмов
Сибирский журнал индустриальной математики. 2022. Т.25. №4. С.193-205. DOI: 10.33048/SIBJIM.2022.25.415 РИНЦ
Оценки решений дифференциальных уравнений с распределенным запаздыванием, описывающих конкуренцию нескольких видов микроорганизмов
Сибирский журнал индустриальной математики. 2022. Т.25. №4. С.193-205. DOI: 10.33048/SIBJIM.2022.25.415 РИНЦ
Dates:
| Submitted: | Jun 20, 2022 |
| Accepted: | Jun 22, 2022 |
| Published print: | Mar 6, 2023 |
Identifiers:
| Scopus: | 2-s2.0-85150204680 |
| Elibrary: | 59138520 |
| OpenAlex: | W4323344519 |