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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2018, Volume 15, Pages 1198–1215
DOI: https://doi.org/10.17377/semi.2018.15.097 (Mi semr988) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Differentical equations, dynamical systems and optimal control

Asymptotic properties of solutions in a model of antibacterial immune response

M. A. Skvortsovaab

a Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia
b Novosibirsk State University, Pirogova st., 2, 630090, Novosibirsk, Russia
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DOI: https://doi.org/10.17377/semi.2018.15.097
Abstract: In the present paper we consider a model of antibacterial immune response proposed by G.I. Marchuk. The model is described by a system of differential equations with three delays. We study the asymptotic stability of the stationary solution corresponding to a healthy organism. We obtain estimates of the attraction set of this solution and establish estimates of solutions characterizing the stabilization rate at infinity. The results are obtained using a modified Lyapunov–Krasovskii functional.
Keywords: antibacterial immune response, delay differential equations, asymptotic stability, estimates of solutions, attraction set, modified \linebreak Lyapunov–Krasovskii functional.
Funding agency Grant number
Russian Foundation for Basic Research 17-41-543365_р_мол_а
Received June 18, 2018, published October 17, 2018
Bibliographic databases:
Document Type: Article
UDC: 517.929.4
MSC: 34K20,~34K60
Language: Russian
Citation: M. A. Skvortsova, “Asymptotic properties of solutions in a model of antibacterial immune response”, Sib. Èlektron. Mat. Izv., 15 (2018), 1198–1215
Citation in format AMSBIB
\Bibitem{Skv18}
\by M.~A.~Skvortsova
\paper Asymptotic properties of solutions in a model of antibacterial immune response
\jour Sib. \`Elektron. Mat. Izv.
\yr 2018
\vol 15
\pages 1198--1215
\mathnet{http://mi.mathnet.ru/semr988}
\crossref{https://doi.org/10.17377/semi.2018.15.097}
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