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Matematicheskie Trudy, 2019, Volume 22, Number 2, Pages 157–174
DOI: https://doi.org/10.33048/mattrudy.2019.22.209 (Mi mt362) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Stability of linear delay differential equations arising in models of living systems

N. V. Pertsev

Sobolev Institute of Mathematics, Omsk Division, Omsk, 644099 Russia
Full-text PDF (241 kB) Citations (7)
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DOI: https://doi.org/10.33048/mattrudy.2019.22.209
Abstract: We present the results of our study of the stability of the trivial solution to a system of linear delay differential equations decomposable into two subsystems. Each of the subsystems contains matrices of a special form. We establish conditions for the asymptotic stability and nonstability of the trivial solution on the basis of the properties of stable matrices and nondegenerate $M$-matrices. The stability of equilibria for mathematical models in immunology and epidemiology is investigated.
Key words: system of linear delay differential equations, stability of the trivial solution, nonnegative matrix, stable matrix, $M$-matrix, Waževski system of equations, mathematical models in immunology and epidemiology.
Funding agency Grant number
Russian Foundation for Basic Research 18-29-10086_мк
The work was supported by the Russian Foundation for Basic Research (grant 18-29-10086).
Received: 21.10.2018
Revised: 20.11.2018
Accepted: 27.02.2019
English version:
Siberian Advances in Mathematics, 2020, Volume 30, Issue 1, Pages 43–54
DOI: https://doi.org/10.3103/S1055134420010046
Bibliographic databases:
Document Type: Article
UDC: 517.929:57
Language: Russian
Citation: N. V. Pertsev, “Stability of linear delay differential equations arising in models of living systems”, Mat. Tr., 22:2 (2019), 157–174; Siberian Adv. Math., 30:1 (2020), 43–54
Citation in format AMSBIB
\Bibitem{Per19}
\by N.~V.~Pertsev
\paper Stability of~linear delay differential equations arising in~models of~living systems
\jour Mat. Tr.
\yr 2019
\vol 22
\issue 2
\pages 157--174
\mathnet{http://mi.mathnet.ru/mt362}
\crossref{https://doi.org/10.33048/mattrudy.2019.22.209}
\transl
\jour Siberian Adv. Math.
\yr 2020
\vol 30
\issue 1
\pages 43--54
\crossref{https://doi.org/10.3103/S1055134420010046}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85081980295}
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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