Itogi Nauki i Tekhniki. Seriya "Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory"
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Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 2020, Volume 188, Pages 84–105 (Mi into743)  

Estimates of solutions in the model of interaction of populations with several delays

M. A. Skvortsova

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: 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.

Keywords: model of interaction of populations, equation with retarded argument, asymptotic stability, estimate of solution, attraction set, modified Lyapunov–Krasovsky functional

Funding Agency Grant Number
Russian Foundation for Basic Research 18-31-00408
18-29-10086
This work was supported by the Russian Foundation for Basic Research (project Nos. 18-31-00408 and 18-29-10086).


DOI: https://doi.org/10.36535/0233-6723-2020-188-84-105

Full text: PDF file (290 kB)
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UDC: 517.929.4
MSC: 34K20, 34K60, 92D25

Citation: M. A. Skvortsova, “Estimates of solutions in the model of interaction of populations with several delays”, Differential Equations and Mathematical Modeling, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 188, VINITI, Moscow, 2020, 84–105

Citation in format AMSBIB
\Bibitem{Skv20}
\by M.~A.~Skvortsova
\paper Estimates of solutions in the model of interaction of populations with several delays
\inbook Differential Equations and Mathematical Modeling
\serial Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz.
\yr 2020
\vol 188
\pages 84--105
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into743}
\crossref{https://doi.org/10.36535/0233-6723-2020-188-84-105}


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