Journal of Mathematical Sciences

, Volume 155, Issue 6, pp 894–907

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


    • Department of Mechanics and MathematicsM. V. Lomonosov Moscow State University
  • I. N. Belova
    • A. M. Oboukhov Institute of Atmospheric PhysicsRAS

DOI: 10.1007/s10958-008-9249-2

Cite this article as:
Logofet, D.O. & Belova, I.N. J Math Sci (2008) 155: 894. doi:10.1007/s10958-008-9249-2


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.

Copyright information

© Springer Science+Business Media, Inc. 2008