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Chelyabinskiy Fiziko-Matematicheskiy Zhurnal, 2024, Volume 9, Issue 4, Pages 634–649
DOI: https://doi.org/10.47475/2500-0101-2024-9-4-634-649
(Mi chfmj409)
 

Mathematics

Global stability and estimates for solutions in a model of population dynamics with delay

M. A. Skvortsovaab

a Sobolev Institute of Mathematics SB RAS, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia
References:
Abstract: We consider a model of the isolated population dynamics described by a delay differential equation. We study the case when the model has no more than two equilibrium points corresponding to the complete extinction of the population and to the constant positive population size. We indicate conditions for the right side of the equation, under which solutions are stabilized to equilibrium points for arbitrary non-negative initial data. We obtain estimates for the stabilization rate depending on the coefficients of the equation, the nonlinear function from the right side of the equation, and the function at the initial time interval. The established estimates characterize the rate of population extinction and the rate of stabilization of the population to a constant value. The results are obtained using Lyapunov–Krasovskii functionals.
Keywords: population dynamics, delay differential equation, equilibrium point, asymptotic stability, estimates for solutions, Lyapunov–Krasovskii functional.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FWNF-2022-0008
The study was carried out within the framework of the state contract of the Sobolev Institute of Mathematics (project no. FWNF-2022-0008).
Received: 25.07.2024
Revised: 16.09.2024
Document Type: Article
UDC: 517.929.4
Language: Russian
Citation: M. A. Skvortsova, “Global stability and estimates for solutions in a model of population dynamics with delay”, Chelyab. Fiz.-Mat. Zh., 9:4 (2024), 634–649
Citation in format AMSBIB
\Bibitem{Skv24}
\by M.~A.~Skvortsova
\paper Global stability and estimates for solutions in a model of population dynamics with delay
\jour Chelyab. Fiz.-Mat. Zh.
\yr 2024
\vol 9
\issue 4
\pages 634--649
\mathnet{http://mi.mathnet.ru/chfmj409}
\crossref{https://doi.org/10.47475/2500-0101-2024-9-4-634-649}
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