, Volume 155, Issue 6, pp 894-907
Date: 22 Nov 2008

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

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Matrix models of age-and/or stage-structured population dynamics 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.

Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 13, No. 4, pp. 145–164, 2007.