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

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Authors

Banasiak, Jacek

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South Ural State University

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.

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Keywords

Population theory, Natchez civilisation, Convex cone, Perron-Frobenius theory, Viability cone

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Citation

Banasiak, J. 2018, 'Population models with projection matrix with some negative entries a solution to the natchez paradox', Bulletin of the South Ural State University, Series: Mathematical Modelling, Programming and Computer Software, vol. 11, no. 3, pp. 18-28.