This article is cited in 1 paper

MATHEMATICS

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

M. V. Nikolaev^ab, A. A. Nikitin^ac, U. Dieckmann<sup>def

a</sup> 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

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.

UDC: 517.968.43

Presented: I. A. Sokolov
Received: 31.08.2023
Revised: 14.11.2023
Accepted: 15.11.2023

DOI: 10.31857/S2686954324010074

 English version: Doklady Mathematics, 2024, 109, 33–37

Bibliographic databases:

•