FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2007, VOLUME 13, NUMBER 4, PAGES 145-164

Nonnegative matrices as a tool to model population dynamics:
Classical models and contemporary expansions

D. O. Logofet
I. N. Belova

Abstract

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Matrix models of age- or/and stage-structured populations rest upon the Perron--Frobenius theorem for nonnegative matrices, and the life cycle graph for individuals of a given biological species plays a major role in model construction and analysis. A summary of classical results in the theory of matrix models for population dynamics is presented, and generalizations are proposed, which have been motivated by a need to account for an additional structure, i.e., to classify individuals not only by age, but also by an additional (discrete) characteristic: size, physiological status, stage of development, etc.

Location: http://mech.math.msu.su/~fpm/eng/k07/k074/k07408h.htm
Last modified: November 28, 2007