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Mathematical notes of NEFU, 2016, Volume 23, Issue 2, Pages 108–120 (Mi svfu27)  
This article is cited in 4 scientific papers (total in 4 papers)

Mathematics

Stability of solutions in the predator-prey model with delay

M. A. Skvortsovaab

a Sobolev Institute of Mathematics, Akademika Koptyuga ave., 4, Novosibirsk, Russia
b Novosibirsk State University, Pirogova st., 2, Novosibirsk 630090, Russia
Full-text PDF (273 kB) Citations (4)
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Abstract: We consider a system of delay differential equations describing the interaction between two populations the predators and prey. We study the asymptotic stability of stationary solutions to this system. Using the modified Lyapunov-Krasovskii functional we establish estimates for solutions characterizing the rate of convergence to the stationary solutions.
Keywords: predator-prey model, delay differential equations, asymptotic stability, characteristic quasipolynomial, estimates for solutions, modified Lyapunov-Krasovskii functional.
Funding agency Grant number
Russian Foundation for Basic Research 15-01-00745
Received: 15.05.2016
Bibliographic databases:
Document Type: Article
UDC: 517.929.4
Language: Russian
Citation: M. A. Skvortsova, “Stability of solutions in the predator-prey model with delay”, Mathematical notes of NEFU, 23:2 (2016), 108–120
Citation in format AMSBIB
\Bibitem{Skv16}
\by M.~A.~Skvortsova
\paper Stability of solutions in the predator-prey model with delay
\jour Mathematical notes of NEFU
\yr 2016
\vol 23
\issue 2
\pages 108--120
\mathnet{http://mi.mathnet.ru/svfu27}
\elib{https://elibrary.ru/item.asp?id=27507487}
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  • https://www.mathnet.ru/eng/svfu27
  • https://www.mathnet.ru/eng/svfu/v23/i2/p108
    • This publication is cited in the following 4 articles:
    1. M. A. Skvortsova, T. Yskak, “Otsenki reshenii differentsialnykh uravnenii s raspredelennym zapazdyvaniem, opisyvayuschikh konkurentsiyu neskolkikh vidov mikroorganizmov”, Sib. zhurn. industr. matem., 25:4 (2022), 193–205  mathnet  crossref
    2. M. A. Skvortsova, T. Yskak, “Asymptotic behavior of solutions in one predator–prey model with delay”, Siberian Math. J., 62:2 (2021), 324–336  mathnet  crossref  crossref  isi  elib
    3. M. A. Skvortsova, “Otsenki reshenii v modeli vzaimodeistviya populyatsii s neskolkimi zapazdyvaniyami”, Differentsialnye uravneniya i matematicheskoe modelirovanie, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 188, VINITI RAN, M., 2020, 84–105  mathnet  crossref
    4. M. A. Skvortsova, “Otsenki reshenii v modeli khischnik-zhertva s zapazdyvaniem”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 25 (2018), 109–125  mathnet  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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