Geodesic
``Nonlinear skeletons'' in the spatio-temporal ecological models
Matematičeskoe modelirovanie, Tome 23 (2011) no. 2, pp. 125-147.

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That many families of the biological competition models turn out to be convex compact (in a certain function space), which extreme points allow the exact description is discovered. The corresponding to extreme point to models (“nonlinear skeletons”) are made enough simply so for them possible it is enough full study as temporary, so and spatial effect in dynamics of competitors. The mathematical base of the study are a geometric methods of the nonlinear analysis (the monotonous operators theory) and computer experiments with models.
Keywords: discrete models, competition, stability.
Mots-clés : population, migration, matrix 
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V. G. Il'ichev. ``Nonlinear skeletons'' in the spatio-temporal ecological models. Matematičeskoe modelirovanie, Tome 23 (2011) no. 2, pp. 125-147. http://geodesic.mathdoc.fr/item/MM_2011_23_2_a9/

[1] Vance R. R., Coddington E. A., “A nonautonomus model of population growth”, J. Math. Biology, 27:5 (1989), 491–506 | DOI | MR | Zbl

[2] Armstrong R. A., Mc. Gehee R., “Coexistence of species competing for shared resources”, Theor. Pop. Biol., 9:3 (1976), 317–328 | DOI | MR | Zbl

[3] Felps R., Lektsii o teoremakh Shoke, Mir, M., 1968, 112 pp.

[4] Ilichev V. G., “Vypuklye struktury v modelyakh ekologii”, Matematicheskoe modelirovanie, 19:4 (2007), 90–102 | MR | Zbl

[5] Marri Dzh., Nelineinye differentsialnye uravneniya v biologii. Lektsii o modelyakh, Mir, M., 1983, 397 pp.

[6] Samarskii A. A., Mikhailov A. P., Matematicheskoe modelirovanie, Fizmatlit, M., 2005, 316 pp.

[7] Svirezhev Yu. M., Nelineinye volny, dissipativnye struktury i katastrofy v ekologii, Nauka, M., 1987, 365 pp. | MR | Zbl

[8] Zhabotinskii A. M., Kontsentratsionnye kolebaniya, Nauka, M., 1974, 178 pp.

[9] Berezovskaya F. S., Karev G. P., “Bifurkatsii beguschikh voln v modelyakh populyatsii s taksisom”, Uspekhi fizicheskikh nauk, 169:9 (1999), 1011–1024

[10] Tyutyunov Yu. V., Sapukhina N. Yu., Morgulis A. B., Govorukhin V. N., “Matematicheskaya model aktivnykh migratsii kak strategiya pitaniya v troficheskikh soobschestvakh”, Zhurnal obschei biologii, 62:3 (2001), 253–262

[11] Ilichev V. G., “Fragment matematicheskoi teorii konkurentsii biologicheskikh vidov v peremennoi srede”, Differentsialnye uravneniya, 27:3 (1991), 437–447 | MR

[12] Ilichev V. G., “O tekhnologii postroeniya imitatsionnykh modelei ekologicheskikh sistem. Mekhanizmy adaptatsii”, Matematicheskoe modelirovanie, 4:3 (1992), 11–19 | MR | Zbl

[13] Arnold V. I., Obyknovennye differentsialnye uravneniya, Nauka, M., 1984, 271 pp. | MR

[14] Krasnoselskii M. A., Zabreiko P. P., Geometricheskie metody nelineinogo analiza, Nauka, M., 1975, 510 pp. | MR

[15] Roberts F. S., Diskretnye matematicheskie modeli s prilozheniem k sotsialnym, biologicheskim i ekologicheskim zadacham, Nauka, M., 1986, 495 pp. | MR | Zbl

[16] Bellman R., Vvedenie v teoriyu matrits, Nauka, M., 1976, 351 pp. | MR

[17] Ilichev V. G., Ustoichivost, adaptatsiya i upravlenie v ekologicheskikh sistemakh, Fizmatlit, M., 2009, 192 pp.