Journal of Mathematical Sciences

, Volume 155, Issue 6, pp 894–907 | Cite as

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



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.


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Copyright information

© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  1. 1.Department of Mechanics and MathematicsM. V. Lomonosov Moscow State UniversityMoscowRussia
  2. 2.A. M. Oboukhov Institute of Atmospheric PhysicsRASMoscowRussia

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