Modelling dynamics of the limited population with age and sex structure
Matematičeskoe modelirovanie, Tome 22 (2010) no. 11, pp. 65-78.

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We investigate the three-componental model of population number dynamics characterized a regular reproduction season. In this model we account for a population sex and age structure and density dependent effects acting on survival rate of a younger age class. We consider particular cases of the model depending on whether various correlation of population parameters. We research transition scenarios from the stability to cyclic and irregular modes of number dynamics. We formulate informative conclusions about sex structure role for processes of population dynamics and self-organizing.
Keywords: population models equations, discrete-time systems, age and sex structure, density-dependent, stability
Mots-clés : bifurcations, dynamic modes, chaos.
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E. Ya. Frisman; O. L. Revutskaya; G. P. Neverova. Modelling dynamics of the limited population with age and sex structure. Matematičeskoe modelirovanie, Tome 22 (2010) no. 11, pp. 65-78. http://geodesic.mathdoc.fr/item/MM_2010_22_11_a5/

[1] Leslie P. H., “On the use of matrices in certain population mathematics”, Biometrika, 33:3 (1945), 183–212 | DOI | MR | Zbl

[2] Lefkovitch L. P., “The study of population growth in organisms grouped by stages”, Biometrics, 21 (1965), 1–18 | DOI

[3] Logofet D. O., Belova I. N., “Neotritsatelnye matritsy kak instrument modelirovaniya dinamiki populyatsii: klassicheskie modeli i sovremennye obobscheniya”, Fundamentalnaya i prikladnaya matematika, 13:4 (2007), 145–164 | MR | Zbl

[4] Hastings A., “Age dependent dispersal is not a simple process: Density dependence, stability, and chaos”, Theor. Popul. Biol., 41:3 (1992), 388–400 | DOI | Zbl

[5] Lebreton J. D., “Demographic Models for Subdivided Populations: The Renewal Equation Approach”, Theor. Popul. Biol., 49:3 (1996), 291–313 | DOI | Zbl

[6] Kooi B. W., Kooijman S. A. L. M., “Discrete Event versus Continuous Approach to Reproduction in Structured Population Dynamics”, Theor. Popul. Biol., 56:1 (1999), 91–105 | DOI | Zbl

[7] Charlesworth B., “Natural selection on multivariate traits in age-structured populations”, Proc. R. Soc. Lond., 251 (1993), 47–52 | DOI

[8] Greenman J. V., Benton T. G., Boots M., White A. R., “The evolution of oscillatory behavior in age-structured species”, The American Naturalist, 166:1 (2005), 68–78 | DOI

[9] Skaletskaya E. I., Frisman E. Ya., Kuzin A. E., “Matematicheskoe modelirovanie dinamiki chislennosti severnogo morskogo kotika. Prosteishaya model lokalnoi populyatsii”, Zhurnal obschei biologii, 41:2 (1980), 270–278

[10] Frisman E. Ya., Skaletskaya E. I., Kuzyn A. E., “A mathematical model of the population dynamics of a local northern fur seal with seal herd”, Ecological Modelling, 16 (1982), 151–172 | DOI

[11] Gaillard J.-M., Festa-Bianchet M., Yoccoz N. G., “Population dynamics of large herbivores: variable recruitment with constant adult survival”, Trends in Ecology and Evolution, 13 (1998), 58–63 | DOI

[12] Tripet F., Richner H., “Density-dependent processes in the population dynamics of a bird ectoparasite Ceratophyllus gallinae”, Ecology, 80 (1999), 1267–1277

[13] Ashley M. V., Willson M. F., Pergams O. R. W., O'Dowd D. J., Gende S. M., Brown J. S., “Evolutionary enlightened management”, Biological Conservation, 111 (2003), 115–123 | DOI

[14] Stockwell C. A., Hendry A. P., Kinnison M. T., “Contemporary evolution meets conservation biology”, Trends in Ecology and Evolution, 18 (2003), 94–101 | DOI

[15] Bolshakov V. N., Kubantsev B. S., Polovaya struktura populyatsii mlekopitayuschikh i ee dinamika, Nauka, M., 1984, 233 pp.

[16] Frisman E. Ya., “Strannye attraktory v prosteishikh modelyakh dinamiki chislennosti populyatsii s vozrastnoi strukturoi”, Doklady RAN, 338:2 (1994), 282–286 | Zbl

[17] Frisman E. Ya., Skaletskaya E. I., “Strannye attraktory v prosteishikh modelyakh dinamiki chislennosti biologicheskikh populyatsii”, Obozrenie prikladnoi i promyshlennoi matematiki, 1:6 (1994), 988–1008 | Zbl

[18] Neimark Yu. I., Landa P. S., Stokhasticheskie i khaoticheskie kolebaniya, Nauka, M., 1987, 424 pp. | MR

[19] Inchausti P., Ginzburg L. R., “Small mammals cycles in northern Europe: patterns and evidence for the maternal effect hypothesis”, J. of Animal Ecology, 67 (1998), 180–194 | DOI