Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
GLOBAL STABILITY AND ESTIMATES FOR SOLUTIONS IN A MODEL OF POPULATION DYNAMICS WITH DELAY. / Скворцова, Мария Александровна.
в: Chelyabinsk Physical and Mathematical Journal, Том 9, № 4, 2024, стр. 634-649.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
}
TY - JOUR
T1 - GLOBAL STABILITY AND ESTIMATES FOR SOLUTIONS IN A MODEL OF POPULATION DYNAMICS WITH DELAY
AU - Скворцова, Мария Александровна
N1 - The study was carried out within the framework of the state contract of the Sobolev Institute of Mathematics (project no. FWNF-2022-0008).
PY - 2024
Y1 - 2024
N2 - 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.
AB - 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.
UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85208747867&origin=inward&txGid=d7f372be74c8d71ee53c953622e445e7
M3 - статья
VL - 9
SP - 634
EP - 649
JO - Chelyabinsk Physical and Mathematical Journal
JF - Chelyabinsk Physical and Mathematical Journal
SN - 2500-0101
IS - 4
ER -
ID: 61301941