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Abstract <p> The model of population dynamics of a single-species biological community proposed byW. Dieckmann and R. Law is considered. Changes in the population are described by a system ofintegro-differential equations, which characterizes the dynamics of spatial moments and in thestate of equilibrium is reduced to a nonlinear integral equation. The solvability of this equation isstudied, according to which the solution of the original system is written out, for whicha nonlinear integral operator is constructed and the problem of finding its fixed point is solved.Sufficient conditions for the existence of a nontrivial solution are established. An analyticalexample of the values of biological parameters that satisfy these conditions is given.</p>

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Solvability of a System of Nonlinear Integral Equations with Piecewise Constant Kernels

  • 期刊论文

  • 发表日期：

    2025年9月1日

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  • P. S. Nesterenko,
  • A. A. Nikitin,
  • M. V. Nikolaev

摘要

Abstract

The model of population dynamics of a single-species biological community proposed byW. Dieckmann and R. Law is considered. Changes in the population are described by a system ofintegro-differential equations, which characterizes the dynamics of spatial moments and in thestate of equilibrium is reduced to a nonlinear integral equation. The solvability of this equation isstudied, according to which the solution of the original system is written out, for whicha nonlinear integral operator is constructed and the problem of finding its fixed point is solved.Sufficient conditions for the existence of a nontrivial solution are established. An analyticalexample of the values of biological parameters that satisfy these conditions is given.