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

dc.contributor.authorBanasiak, Jacek
dc.contributor.emailjacek.banasiak@up.ac.zaen_ZA
dc.date.accessioned2019-05-09T12:13:14Z
dc.date.available2019-05-09T12:13:14Z
dc.date.issued2018-08
dc.description.abstractIn 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.en_ZA
dc.description.departmentMathematics and Applied Mathematicsen_ZA
dc.description.librarianam2019en_ZA
dc.description.sponsorshipThe research was supported by the National Research Foundation of South Africa under Grant NN. 00317.en_ZA
dc.description.sponsorshipThe National Research Foundation of South Africa under Grant NN. 00317.en_ZA
dc.description.urihttp://mmp.vestnik.susu.ru/page/en/greeten_ZA
dc.identifier.citationBanasiak, 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.en_ZA
dc.identifier.issn2071-0216 (print)
dc.identifier.issn2308-0256 (online)
dc.identifier.other10.14529/mmp180302
dc.identifier.urihttp://hdl.handle.net/2263/69077
dc.language.isoenen_ZA
dc.publisherSouth Ural State Universityen_ZA
dc.rights© South Ural State University. All rights reserved.en_ZA
dc.subjectPopulation theoryen_ZA
dc.subjectNatchez civilisationen_ZA
dc.subjectConvex coneen_ZA
dc.subjectPerron-Frobenius theoryen_ZA
dc.subjectViability coneen_ZA
dc.titlePopulation models with projection matrix with some negative entries a solution to the natchez paradoxen_ZA
dc.typeArticleen_ZA

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