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Vestnik YuUrGU. Ser. Mat. Model. Progr., 2018, Volume 11, Issue 3, Pages 18–28 (Mi vyuru441)  

Mathematical Modelling

Population models with projection matrix with some negative entries — a solution to the Natchez paradox

J. Banasiak

University of Pretoria, South Africa

Abstract: In this note we consider the population the model of which, derived on the basis of ethnographical accounts, includes a projection matrix with both positive and negative entries. Interpreting the eventually negative trajectories as representing the collapse of the population, we use some classical tools from convex analysis to determine a cone containing the initial conditions that give rise to the persistence of both the population and its social structure.

Keywords: population theory; Natchez civilisation; convex cone; Perron–Frobenius theory; viability cone.

Funding Agency Grant Number
National Research Foundation of South Africa 00317
The research was supported by the National Research Foundation of South Africa under Grant NN. 00317.


DOI: https://doi.org/10.14529/mmp180302

Full text: PDF file (318 kB)
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Document Type: Article
UDC: 62-501.42
MSC: 92D25
Received: 20.06.2018
Language: English

Citation: J. Banasiak, “Population models with projection matrix with some negative entries — a solution to the Natchez paradox”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 11:3 (2018), 18–28

Citation in format AMSBIB
\Bibitem{Ban18}
\by J.~Banasiak
\paper Population models with projection matrix with some negative entries~--- a solution to the Natchez paradox
\jour Vestnik YuUrGU. Ser. Mat. Model. Progr.
\yr 2018
\vol 11
\issue 3
\pages 18--28
\mathnet{http://mi.mathnet.ru/vyuru441}
\crossref{https://doi.org/10.14529/mmp180302}


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