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Solvability Analysis of the Nonlinear Integral Equations System Arising in the Logistic Dynamics Model in the Case of Piecewise Constant Kernels

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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 L1 norm of the solution and for the closure parameter are obtained.

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REFERENCES

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Funding

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.

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Authors and Affiliations

  1. Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Moscow, Russia

    M. V. Nikolaev & A. A. Nikitin

  2. Moscow Center for Fundamental and Applied Mathematics, Moscow, Russia

    M. V. Nikolaev

  3. Trapeznikov Institute of Control Sciences of the Russian Academy of Sciences, Moscow, Russia

    A. A. Nikitin

  4. Okinawa Institute of Science and Technology Graduate University, Onna, Japan

    U. Dieckmann

  5. International Institute for Applied Systems Analysis, Laxenburg, Austria

    U. Dieckmann

  6. Graduate University for Advanced Studies, Hayama, Japan

    U. Dieckmann

Authors
  1. M. V. Nikolaev
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  2. A. A. Nikitin
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  3. U. Dieckmann
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Corresponding authors

Correspondence to M. V. Nikolaev, A. A. Nikitin or U. Dieckmann.

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The authors of this work declare that they have no conflicts of interest.

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Translated by I. Ruzanova

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Nikolaev, M.V., Nikitin, A.A. & Dieckmann, U. Solvability Analysis of the Nonlinear Integral Equations System Arising in the Logistic Dynamics Model in the Case of Piecewise Constant Kernels. Dokl. Math. (2024). https://doi.org/10.1134/S1064562424701783

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  • DOI: https://doi.org/10.1134/S1064562424701783

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