On the stability of the equilibrium problem solution in the multispecies Dieckmann–Law model

Recieved: 03/29/2026

Accepted: 05/20/2026

Keywords: mathematical biology, nonlinear integral equations, functional analysis

Available in the on-line version with: 15.09.2026

To cite this article

Nikolaev M.V. On the stability of the equilibrium problem solution in the multispecies Dieckmann–Law model. // Moscow University Journal. Series 15. Computational Mathematics and Cybernetics. 2026. N 3, p.66-78 https://doi.org/10.55959/MSU/0137–0782–15–2026–50–3–66–78.

This work is licensed under a Сreative Commons Atribiution - NonCommercial 4.0 International (CC BY-NC 4.0)

Nikolaev M.V. (Lomonosov Moscow State University (MSU))

Abstract

The paper examines a multispecies model of population dynamics of biological communities proposed by U. Dieckmann and R. Law in a space of arbitrary dimension. A system of nonlinear integral equations, arising in the problem of finding the equilibrium state after the three-parameter power-2 closure of the third spatial moments, is investigated. After preliminary transformations, this system is represented as a single operator equation in a Banach space of functional matrices of a special form, which allows describing the equilibrium state as the fixed point of a certain operator. Conditions are formulated that are sufficient to ensure that small changes in the closure parameters lead to small changes in the fixed points set of the operator, in terms of the distance induced by the norm of the Banach space.