Geodesic
Nonnegative matrices as a~tool to model population dynamics: Classical models and contemporary expansions
Fundamentalʹnaâ i prikladnaâ matematika, Tome 13 (2007) no. 4, pp. 145-164

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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. 
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     author = {D. O. Logofet and I. N. Belova},
     title = {Nonnegative matrices as a~tool to model population dynamics: {Classical} models and contemporary expansions},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {145--164},
     publisher = {mathdoc},
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     number = {4},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2007_13_4_a7/}
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D. O. Logofet; I. N. Belova. Nonnegative matrices as a~tool to model population dynamics: Classical models and contemporary expansions. Fundamentalʹnaâ i prikladnaâ matematika, Tome 13 (2007) no. 4, pp. 145-164. http://geodesic.mathdoc.fr/item/FPM_2007_13_4_a7/