Geodesic
Population models with projection matrix with some negative entries — a solution to the Natchez paradox
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 11 (2018) no. 3, pp. 18-28 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     title = {Population models with projection matrix with some negative entries~{\textemdash} a solution to the {Natchez} paradox},
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J. Banasiak. Population models with projection matrix with some negative entries — a solution to the Natchez paradox. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 11 (2018) no. 3, pp. 18-28. http://geodesic.mathdoc.fr/item/VYURU_2018_11_3_a1/

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