This article is cited in 1 paper

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.

UDC: 62-501.42

MSC: 92D25

Received: 20.06.2018

Language: English

DOI: 10.14529/mmp180302

Bibliographic databases:

•