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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2022, Volume 507, Pages 46–50
DOI: https://doi.org/10.31857/S2686954322600604 (Mi danma317) 		 
MATHEMATICS

Stability analysis of the solution to a system of nonlinear integral equations arising in a logistic dynamics model

M. V. Nikolaevab, A. A. Nikitinac, U. Dieckmanndef

a Lomonosov Moscow State University
b Moscow Center for Fundamental and Applied Mathematics, Moscow, Russia
c Trapeznikov Institute of Control Sciences of the Russian Academy of Sciences, Moscow, Russia
d Okinawa Institute of Science and Technology Graduate University, Onna, Japan
e International Institute for Applied Systems Analysis, Laxenburg, Austria
f Graduate University for Advanced Studies, Hayama, Japan
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DOI: https://doi.org/10.31857/S2686954322600604
Abstract: In this paper, we analyze a system of nonlinear integral equations resulting from the three-parameter closure of the third spatial moments in the logistic dynamics model of U. Dieckmann and R. Law in the multi-species case. Specifically, the conditions under which the solution of this system is stable with respect to the closure parameters are investigated. To do this, the initial system of equations is represented as a single operator equation in a special Banach space, after which the generalized fixed point principle is applied.
Keywords: functional analysis, nonlinear integral equations, mathematical biology.
Funding agency Grant number
Russian Science Foundation 22-11-00042
Moscow Center of Fundamental and Applied Mathematics 075-15-2022-284
The results in Sections 1 and 2 were obtained by Nikitin with financial support from the Russian Science Foundation, project no. 22-11-00042. The other results were obtained by all the authors with support from the Ministry of Science and Higher Education of the Russian Federation within the framework of the program of the Moscow Center for Fundamental and Applied Mathematics, agreement no. 075-15-2022-284.
Presented: I. A. Sokolov
Received: 29.09.2022
Revised: 13.11.2022
Accepted: 17.11.2022
English version:
Doklady Mathematics, 2022, Volume 106, Issue 3, Pages 445–448
DOI: https://doi.org/10.1134/S1064562422700144
Bibliographic databases:
Document Type: Article
UDC: 517.968.43
Language: Russian
Citation: M. V. Nikolaev, A. A. Nikitin, U. Dieckmann, “Stability analysis of the solution to a system of nonlinear integral equations arising in a logistic dynamics model”, Dokl. RAN. Math. Inf. Proc. Upr., 507 (2022), 46–50; Dokl. Math., 106:3 (2022), 445–448
Citation in format AMSBIB
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\by M.~V.~Nikolaev, A.~A.~Nikitin, U.~Dieckmann
\paper Stability analysis of the solution to a system of nonlinear integral equations arising in a logistic dynamics model
\jour Dokl. RAN. Math. Inf. Proc. Upr.
\yr 2022
\vol 507
\pages 46--50
\mathnet{http://mi.mathnet.ru/danma317}
\crossref{https://doi.org/10.31857/S2686954322600604}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4563845}
\elib{https://elibrary.ru/item.asp?id=49991283}
\transl
\jour Dokl. Math.
\yr 2022
\vol 106
\issue 3
\pages 445--448
\crossref{https://doi.org/10.1134/S1064562422700144}
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