D. O. Logofet, I. N. Klochkova, “Mathematics of the Lefkovitch model: the reproductive potential and asymptotic cycles”, Mat. Model., 14:10 (2002), 116

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Matematicheskoe modelirovanie, 2002, Volume 14, Number 10, Pages 116–126 (Mi mm545)

This article is cited in 15 scientific papers (total in 15 papers)

Mathematics of the Lefkovitch model: the reproductive potential and asymptotic cycles

D. O. Logofet^a, I. N. Klochkova^b

^a A. M. Obukhov Institute of Atmospheric Physics, Russian Academy of Sciences
^b M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

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Abstract: A discrete-time model of discrete-stage-structured population dynamics is studied which generalises the classic Leslie model. The notion of reproductive potential is defined via the characteristic polynomial of the matrix of demographic parameters (Lefkovitch matrix), and the reproductive potential theorem is proved. A model where the demographic parameters are season-specific is proved to have no cycles in its annual dynamics, and we have found an inter-seasonal cycle resulting in the equilibrium population structure at the annual time scale. The seasonal model is calibrated on observation data for a population of Aporrectodea caliginosa worms under conditions of rlfear-Moscow localities. We have substituted certain assumptions for uncertainty in the data, and validity of the assumptions can thereafter be judged from the model results amenable to empiric tests.

Received: 01.12.2000

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Language: Russian

Citation: D. O. Logofet, I. N. Klochkova, “Mathematics of the Lefkovitch model: the reproductive potential and asymptotic cycles”, Mat. Model., 14:10 (2002), 116–126

Citation in format AMSBIB

\Bibitem{LogKlo02}

\by D.~O.~Logofet, I.~N.~Klochkova

\paper Mathematics of the Lefkovitch model: the reproductive potential and asymptotic cycles

\jour Mat. Model.

\yr 2002

\vol 14

\issue 10

\pages 116--126

\mathnet{http://mi.mathnet.ru/mm545}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1989787}

\zmath{https://zbmath.org/?q=an:1011.92041}

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https://www.mathnet.ru/eng/mm545

https://www.mathnet.ru/eng/mm/v14/i10/p116

This publication is cited in the following 15 articles:

G. P. Neverova, E. Ya. Frisman, “Evolyutsionnaya dinamika dvukhvozrastnoi populyatsii pri plotnostno-zavisimoi regulyatsii vyzhivaemosti starshikh vozrastov”, Matem. biologiya i bioinform., 19:2 (2024), 293–303
Frisman E.Ya., Zhdanova O.L., Kulakov M.P., Neverova G.P., Revutskaya O.L., “Mathematical Modeling of Population Dynamics Based on Recurrent Equations: Results and Prospects. Part i”, Biol. Bull, 48:1 (2021), 1–15
Romanov M.S., Masterov V.B., “Low Breeding Performance of the Steller'S Sea Eagle (Haliaeetus Pelagicus) Causes the Populations to Decline”, Ecol. Model., 420 (2020), 108877
E. Ya. Frisman, M. P. Kulakov, O. L. Revutskaya, O. L. Zhdanova, G. P. Neverova, “Osnovnye napravleniya i obzor sovremennogo sostoyaniya issledovanii dinamiki strukturirovannykh i vzaimodeistvuyuschikh populyatsii”, Kompyuternye issledovaniya i modelirovanie, 11:1 (2019), 119–151
Logofet D.O., “Polyvariant Ontogeny in Plants: When the Second Eigenvalue Plays a Primary Role”, Advanced Mathematical Methods in Biosciences and Applications, Steam-H Science Technology Engineering Agriculture Mathematics & Health, eds. Berezovskaya F., Toni B., Springer International Publishing Ag, 2019, 111–130
Logofet D.O., “Calamagrostis Model Revisited: Matrix Calibration as a Constraint Maximization Problem”, Ecol. Model., 254 (2013), 71–79
D. O. Logofet, “Projection matrices revisited: a potential-growth indicator and the merit of indication”, J. Math. Sci., 193:5 (2013), 671–686
Nedorezov L.V., Utyupin Yu.V., “Nepreryvno-diskretnye modeli dinamiki chislennosti populyatsii”, Ekologiya. Seriya analiticheskikh obzorov mirovoi literatury, 2011, no. 95, 1–234
Poikolainen V.V., Sigovtsev G.S., “Detalizirovannaya model dinamiki strukturirovannoi populyatsii”, Uchenye zapiski Petrozavodskogo gosudarstvennogo universiteta. Seriya: Estestvennye i tekhnicheskie nauki, 2011, no. 6, 91–96
Logofet D.O., “Svirezhev's substitution principle and matrix models for dynamics of populations with complex structures”, Zhurnal Obshchei Biologii, 71:1 (2010), 30–40
Logofet, DO, “Convexity in projection matrices: Projection to a calibration problem”, Ecological Modelling, 216:2 (2008), 217
D. O. Logofet, I. N. Belova, “Nonnegative matrices as a tool to model population dynamics: Classical models and contemporary expansions”, J. Math. Sci., 155:6 (2008), 894–907
Logofet, DO, “Structure and dynamics of a clonal plant population: Classical model results in a non-classic formulation”, Ecological Modelling, 192:1–2 (2006), 95
D. O. Logofet, “Tri istochnika i tri sostavnye chasti formalizma populyatsii s diskretnoi stadiinoi i vozrastnoi strukturami”, Matem. modelirovanie, 14:12 (2002), 11–22
Ulanova, NG, “The structure and dynamics of a woodreed Calamagrostis canescens population: a modelling approach”, Zhurnal Obshchei Biologii, 63:6 (2002), 509

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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