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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2024, Volume 515, Pages 44–49
DOI: https://doi.org/10.31857/S2686954324010074 (Mi danma491) 		 
MATHEMATICS

Solvability analysis of the nonlinear integral equations system arising in the logistic dynamics model in the case of piecewise constant kernels

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

a Lomonosov Moscow State University
b Moscow Center for Fundamental and Applied Mathematics
c V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow
d Okinawa Institute of Science and Technology
e International Institute for Applied Systems Analysis, Laxenburg
f The Graduate University for Advanced Studies
DOI: https://doi.org/10.31857/S2686954324010074
Abstract: A nonlinear integral equation arising from a parametric closure of the third spatial moment in the single-species model of logistic dynamics of U. Dieckmann and R. Law is analyzed. The case of piecewise constant kernels is studied, which is important for further computer modeling. Sufficient conditions are found that guarantee the existence of a nontrivial solution to the equilibrium equation. The use of constant kernels makes it possible to obtain more accurate results compared to earlier works, in particular, more accurate estimates for the $L_1$ norm of the solution and for the closure parameter are obtained.
Keywords: functional analysis, nonlinear integral equations, mathematical biology.
Funding agency Grant number
Russian Science Foundation 22-11-00042
Ministry of Science and Higher Education of the Russian Federation 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: 31.08.2023
Revised: 14.11.2023
Accepted: 15.11.2023
English version:
Doklady Mathematics, 2024, Volume 109, Pages 33–37
DOI: https://doi.org/10.1134/S1064562424701783
Bibliographic databases:
Document Type: Article
UDC: 517.968.43
Language: Russian
Citation: M. V. Nikolaev, A. A. Nikitin, U. Dieckmann, “Solvability analysis of the nonlinear integral equations system arising in the logistic dynamics model in the case of piecewise constant kernels”, Dokl. RAN. Math. Inf. Proc. Upr., 515 (2024), 44–49; Dokl. Math., 109 (2024), 33–37
Citation in format AMSBIB
\Bibitem{NikNikDie24}
\by M.~V.~Nikolaev, A.~A.~Nikitin, U.~Dieckmann
\paper Solvability analysis of the nonlinear integral equations system arising in the logistic dynamics model in the case of piecewise constant kernels
\jour Dokl. RAN. Math. Inf. Proc. Upr.
\yr 2024
\vol 515
\pages 44--49
\mathnet{http://mi.mathnet.ru/danma491}
\crossref{https://doi.org/10.31857/S2686954324010074}
\elib{https://elibrary.ru/item.asp?id=67973248}
\transl
\jour Dokl. Math.
\yr 2024
\vol 109
\pages 33--37
\crossref{https://doi.org/10.1134/S1064562424701783}
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