Abstract:
We study the question of determining all those parameters for which all positive solutions of the logistic equation with delay tend to zero as t→∞. The well-known Wright conjecture [1] on the estimation of the set of such parameters is proved. A methodology has been developed that makes it possible to consistently refine this estimate.
Keywords:
logistic equation, global stable, delay, one-dimensional mapping, asymptotics of solutions.
Благодарности. Работа выполнена при финансовой поддержке Российского фонда фундаментальных исследований (№18-29-10043) и проекта РНОМЦ (№1.13560.2019/13.1) Министерства науки и высшего образования.
Citation:
S. A. Kaschenko, D. O. Loginov, “Estimation of the region of global stability of the equilibrium state of the logistic equation with delay”, Izv. Vyssh. Uchebn. Zaved. Mat., 2020, no. 9, 39–55; Russian Math. (Iz. VUZ), 64:9 (2020), 34–49
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\by S.~A.~Kaschenko, D.~O.~Loginov
\paper Estimation of the region of global stability of the equilibrium state of the logistic equation with delay
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2020
\issue 9
\pages 39--55
\mathnet{http://mi.mathnet.ru/ivm9610}
\crossref{https://doi.org/10.26907/0021-3446-2020-9-39-55}
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\jour Russian Math. (Iz. VUZ)
\yr 2020
\vol 64
\issue 9
\pages 34--49
\crossref{https://doi.org/10.3103/S1066369X20090042}
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https://www.mathnet.ru/eng/ivm9610
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