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Comments on Mathematical Aspects of the Biró–Néda Model

Author

Listed:
  • Ilda Inácio

    (Centro de Matemática e Aplicações (CMA-UBI), Universidade da Beira Interior, 6201-001 Covilhã, Portugal)

  • José Velhinho

    (Faculdade de Ciências and FibEnTech-UBI, Universidade da Beira Interior, R. Marquês D’Ávila e Bolama, 6201-001 Covilhã, Portugal)

Abstract

We address two mathematical aspects of the Biró–Néda dynamical model, recently applied in the statistical analysis of several and varied complex phenomena. First, we show that a given implicit assumption ceases to be valid outside the most simple and common cases, and we analyze the consequences thereof, in what the formulation of the model and probability conservation is concerned. Second, we revisit the transient behavior in the case of a constant reset rate and a constant or linear growth rate, improving on a previous analysis by including more general initial conditions.

Suggested Citation

  • Ilda Inácio & José Velhinho, 2022. "Comments on Mathematical Aspects of the Biró–Néda Model," Mathematics, MDPI, vol. 10(4), pages 1-10, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:4:p:644-:d:753277
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    References listed on IDEAS

    as
    1. Gere, István & Kelemen, Szabolcs & Tóth, Géza & Biró, Tamás S. & Néda, Zoltán, 2021. "Wealth distribution in modern societies: Collected data and a master equation approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 581(C).
    2. Cardoso, Ben-Hur Francisco & Gonçalves, Sebastián & Iglesias, José Roberto, 2020. "Wealth distribution models with regulations: Dynamics and equilibria," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    3. Néda, Zoltán & Gere, István & Biró, Tamás S. & Tóth, Géza & Derzsy, Noemi, 2020. "Scaling in income inequalities and its dynamical origin," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 549(C).
    4. Zoltan Neda & Istvan Gere & Tamas S. Biro & Geza Toth & Noemi Derzsy, 2019. "Scaling in Income Inequalities and its Dynamical Origin," Papers 1911.02449, arXiv.org, revised Mar 2020.
    5. Zoltán Néda & Levente Varga & Tamás S Biró, 2017. "Science and Facebook: The same popularity law!," PLOS ONE, Public Library of Science, vol. 12(7), pages 1-11, July.
    6. Istvan Gere & Szabolcs Kelemen & Geza Toth & Tamas Biro & Zoltan Neda, 2021. "Wealth distribution in modern societies: collected data and a master equation approach," Papers 2104.04134, arXiv.org.
    7. Cui, Lijie & Lin, Chuandong, 2021. "A simple and efficient kinetic model for wealth distribution with saving propensity effect: Based on lattice gas automaton," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 561(C).
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