TY - JOUR

T1 - Estimates of Solutions in the Model of Interaction of Populations with Several Delays

AU - Skvortsova, M. A.

PY - 2025/2/26

Y1 - 2025/2/26

N2 - We consider a system of differential equations with several delays, which describes the interaction of n species of microorganisms. We obtain sufficient conditions for the asymptotic stability of a nontrivial equilibrium state corresponding to the partial survival of populations. We establish estimates of solutions that characterize the rate of stabilization at infinity and indicate estimates of the attraction set of a given equilibrium state. The results are obtained by using the modified Lyapunov–Krasovsky functional.

AB - We consider a system of differential equations with several delays, which describes the interaction of n species of microorganisms. We obtain sufficient conditions for the asymptotic stability of a nontrivial equilibrium state corresponding to the partial survival of populations. We establish estimates of solutions that characterize the rate of stabilization at infinity and indicate estimates of the attraction set of a given equilibrium state. The results are obtained by using the modified Lyapunov–Krasovsky functional.

KW - 34K20

KW - 34K60

KW - 92D25

KW - asymptotic stability

KW - attraction set

KW - equation with delayed argument

KW - estimate of solution

KW - model of interaction of populations

KW - modified Lyapunov–Krasovsky functional

UR - https://www.mendeley.com/catalogue/aab86005-b8e5-3362-8241-6a310da663b4/

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85218715811&origin=inward&txGid=6044d30b7c8321dc94a2ea9394075c79

U2 - 10.1007/s10958-025-07649-9

DO - 10.1007/s10958-025-07649-9

M3 - Article

JO - Journal of Mathematical Sciences (United States)

JF - Journal of Mathematical Sciences (United States)

SN - 1072-3374

ER -