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Solvability analysis of the nonlinear integral equations system arising in the logistic dynamics model in the piecewise constant kernels case
- Authors: Nikolaev M.V.1,2, Nikitin A.A.1,3, Dieckmann U.4,5,6
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Affiliations:
- Lomonosov Moscow State University
- Moscow Center of Fundamental and Applied Mathematics
- V.A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences
- Okinawa Institute of Science and Technology Graduate University
- International Institute for Applied Systems Analysis
- Graduate University for Advanced Studies
- Issue: Vol 515, No 1 (2024)
- Pages: 44-49
- Section: MATHEMATICS
- URL: https://ruspoj.com/2686-9543/article/view/647924
- DOI: https://doi.org/10.31857/S2686954324010074
- EDN: https://elibrary.ru/ZTSGZU
- ID: 647924
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Abstract
The work is devoted to the analysis of a nonlinear integral equation that arises as a result of parametric closure of the third spatial moment in a single-species model of logistic dynamics by U. Dieckmann and R. Law. The case of piecewise constant kernels is analyzed, which is very important for further computer modeling. Sufficient conditions have been found to guarantee the existence of a nontrivial solution to the equilibrium equation. The use of constant kernels made it possible to obtain more accurate results compared to earlier works, in particular, more accurate estimates were obtained for the norm of the solution, as well as for the closure parameter.
About the authors
M. V. Nikolaev
Lomonosov Moscow State University; Moscow Center of Fundamental and Applied Mathematics
Author for correspondence.
Email: nikolaev.mihail@inbox.ru
Russian Federation, Moscow
A. A. Nikitin
Lomonosov Moscow State University; V.A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences
Email: nikitin@cs.msu.ru
Russian Federation, Moscow
U. Dieckmann
Okinawa Institute of Science and Technology Graduate University; International Institute for Applied Systems Analysis; Graduate University for Advanced Studies
Email: dieckmann@iiasa.ac.at
Japan, Onna; Laxenburg, Austria; Hayama
References
- Law R., Dieckmann U. Moment approximations of individual-based models // The Geometry of Ecological Interactions: Simplifying Spatial Complexity / Ed. by U. Dieckmann, R. Law, J. Metz. Cambridge University Press, 2000. P. 252–270.
- Dieckmann U., Law R. Relaxation projections and the method of moments // The Geometry of Ecological Interactions: Simplifying Spatial Complexity / Ed. by U. Dieckmann, R. Law, J. Metz. Cambridge University Press. 2000. P. 412–455.
- Murrell D.J., Dieckmann U., Law R. On moment closures for population dynamics in continuous space // J. Theor. Biology. 2004. Vol. 229. P. 421–432.
- Красносельский М.А. Два замечания о методе последовательных приближений // УМН. 1955. 10:1(63). С. 123–127.
- Никитин А.А., Николаев М.В. Принцип Лере–Шаудера в применении к исследованию одного нелинейного интегрального уравнения // Дифференциальные уравнения. 2019. Т. 55. С. 1209–1217.
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