TY - JOUR

T1 - Estimates for Solutions of a Biological Model with Infinite Distributed Delay

AU - Iskakov, T. K.

AU - Skvortsova, M. A.

N1 - 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.

PY - 2024/8

Y1 - 2024/8

N2 - 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.

AB - 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.

KW - Lyapunov–Krasovskii functional

KW - asymptotic stability

KW - chemostat

KW - delay differential equations

KW - domain of attraction

KW - equilibrium point

KW - estimates for solutions

KW - infinite distributed delay

KW - species competition model

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85205388707&origin=inward&txGid=c905ca6820122d7cb2d3ec197d8273b6

UR - https://www.mendeley.com/catalogue/0ebf9060-7d3d-3a78-acf9-a1499fd05d00/

UR - https://elibrary.ru/item.asp?id=69921016

U2 - 10.1134/S0965542524700921

DO - 10.1134/S0965542524700921

M3 - Article

VL - 64

SP - 1689

EP - 1703

JO - Computational Mathematics and Mathematical Physics

JF - Computational Mathematics and Mathematical Physics

SN - 0965-5425

IS - 8

ER -