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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
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.
Received: 25.07.2024 Revised: 16.09.2024
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
Linking options:
https://www.mathnet.ru/eng/chfmj409 https://www.mathnet.ru/eng/chfmj/v9/i4/p634
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Abstract page: | 46 | Full-text PDF : | 13 | References: | 15 |
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