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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
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.
Received: 02.04.2024 Revised: 02.04.2024 Accepted: 02.05.2024
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
Linking options:
https://www.mathnet.ru/eng/zvmmf11809 https://www.mathnet.ru/eng/zvmmf/v64/i8/p1409
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