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A Mathematical Model For Population Distribution

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  • Nicholas Elias

    (Democritus University of Thrace, GREECE)

Abstract

In the present paper, an attempt is made to construct a deterministic mathematical simulation for population systems, by which their temporal (equation of motion) and spatiotemporal (equation of distribution) behaviour can be deduced, as solutions of the constitutional differential equations of the system. The generic formulation of the constitutional equations gives the simulation the possibility to expand to several populations, but also to parameters of different nature (say economic), by applying proper transformations according to the inner properties of each parameter. The introduction of the topographical features of such a system can be reduced to a boundary conditions problem, applied to the constitutional differential equations. Two initial applications are analyzed herein, namely a one-dimensional inertial population system, and a one-dimensional dynamic population system, where the external force corresponds to a space of constant curvature. The theoretically predicted behaviors of the population distribution of these systems are compared qualitatively to actual field data, collected from cities around the World.

Suggested Citation

  • Nicholas Elias, 2023. "A Mathematical Model For Population Distribution," Romanian Journal of Regional Science, Romanian Regional Science Association, vol. 17(2), pages 40-65, DECEMBER.
    • Handle: RePEc:rrs:journl:v:17:y:2023:i:2:p:40-65
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    References listed on IDEAS

    as
    1. Daniel Griffith & David Wong, 2007. "Modeling population density across major US cities: a polycentric spatial regression approach," Journal of Geographical Systems, Springer, vol. 9(1), pages 53-75, April.
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    Cited by:

    1. Nicholas Elias, 2024. "A mathematical model for population distribution II: Linear systems," Romanian Journal of Regional Science, Romanian Regional Science Association, vol. 18(2), pages 1-34, December.

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    More about this item

    Keywords

    mathematical simulation; constitutional equations; population distribution.;
    All these keywords.

    JEL classification:

    • Y80 - Miscellaneous Categories - - Related Disciplines - - - Related Disciplines

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