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Stability Analysis of the Solution to a System of Nonlinear Integral Equations Arising in a Logistic Dynamics Model

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Abstract

In this paper, we analyze a system of nonlinear integral equations resulting from the three-parameter closure of the third spatial moments in the logistic dynamics model of U. Dieckmann and R. Law in the multi-species case. Specifically, the conditions under which the solution of this system is stable with respect to the closure parameters are investigated. To do this, the initial system of equations is represented as a single operator equation in a special Banach space, after which the generalized fixed point principle is applied.

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REFERENCES

  1. R. Law and U. Dieckmann, “Moment approximations of individual-based models,” The Geometry of Ecological Interactions: Simplifying Spatial Complexity, Ed. by U. Dieckmann, R. Law, and J. A. J. Metz (Cambridge Univ. Press, Cambridge, 2000), pp. 252–270.

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  2. U. Dieckmann and R. Law, “Relaxation projections and the method of moments,” The Geometry of Ecological Interactions: Simplifying Spatial Complexity, Ed. by U. Dieckmann, R. Law, and J. A. J. Metz (Cambridge Univ. Press, Cambridge, 2000), pp. 412–455.

    Book  MATH  Google Scholar 

  3. D. J. Murrell, U. Dieckmann, and R. Law, “On moment closures for population dynamics in continuous space,” J. Theor. Biol. 229, 421–432 (2004).

    Article  MATH  Google Scholar 

  4. M. A. Krasnosel’skii, “Two remarks on the method of successive approximations,” Usp. Mat. Nauk 10 (1), 123–127 (1955).

    MathSciNet  Google Scholar 

  5. M. V. Nikolaev, A. A. Nikitin, and U. Dieckmann, “Application of a generalized fixed point principle to the study of a system of nonlinear integral equations arising in the population dynamics model,” Differ. Equations 58 (9), 1233–1241 (2022).

    Article  MathSciNet  MATH  Google Scholar 

  6. M. V. Nikolaev, U. Dieckmann, and A. A. Nikitin, “Application of special function spaces to the study of nonlinear integral equations arising in equilibrium spatial logistic dynamics,” Dokl. Math. 104 (1), 188–192 (2021).

    Article  MathSciNet  MATH  Google Scholar 

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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 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. Stability Analysis of the Solution to a System of Nonlinear Integral Equations Arising in a Logistic Dynamics Model. Dokl. Math. 106, 445–448 (2022). https://doi.org/10.1134/S1064562422700144

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  • DOI: https://doi.org/10.1134/S1064562422700144

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